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Learn Properties of tangents
Welcome to one of the most fascinating topics in CBSE Class 10 Mathematics: Circles. Specifically, we are diving into the "Properties of Tangents." Imagine a bicycle wheel rolling on a flat road; the road touches the wheel at exactly one point at any given time. That line, which touches the circle at just a single point without cutting through the inside, is called a tangent. Understanding how tangents interact with circles is a foundational concept in geometry that builds logical reasoning and sets the stage for more advanced mathematical proofs.
The core logic of tangents relies on two foundational theorems. First, the tangent at any point of a circle is perpendicular to the radius drawn to the point of contact. Mathematically, if a tangent touches the circle at point A and the center is O, then the angle formed is exactly 90° (OA ⊥ PA). Second, the lengths of tangents drawn from an external point to a circle are exactly equal. If you pick an external point P and draw two tangents touching the circle at points A and B, the lengths PA and PB will always be identical. This creates a highly symmetrical figure where the line connecting the external point to the center (OP) perfectly bisects the angle between the two tangents.
Let’s look at the diagram above to visualize these properties. The blue circle has a center labeled O, and an external point P sits outside it. Two red lines, PA and PB, represent the tangents touching the circle at points A and B. Notice the green dotted lines—these are the radii (OA and OB). The green square symbol at points A and B highlights our first theorem: the radius is always perpendicular to the tangent at the exact point of contact, creating a perfect 90° right angle. Furthermore, because OA = OB (radii of the same circle), OP is a shared common side, and both have right angles, the two right-angled triangles (ΔOAP and ΔOBP) are perfectly identical (congruent by the RHS rule). This logical proof guarantees our second theorem: the tangent lengths PA and PB are equal, marked by the double red hash lines. In your CBSE Class 10 board exams, you will frequently use these exact properties to find missing angles or calculate lengths in complex geometric figures!
Grasping geometry theorems like the properties of tangents can sometimes feel overwhelming, but mastering them is absolutely crucial for scoring high marks in your board exams. If you find these spatial concepts challenging or want to practice advanced application questions to perfect your skills, UrbanPro is here to help. On the UrbanPro platform, you can connect with highly experienced and verified CBSE Class 10 Mathematics tutors who simplify complex topics through clear, step-by-step guidance. Whether you prefer online interactive classes or local offline tuition near you, explore UrbanPro today to find the perfect math tutor and significantly boost your board exam preparation!
Other Concept Videos for Properties of tangents
Key Properties of Circle Tangents
CBSE - Class 10>Mathematics>Circles>Properties of tangents
Top Tutors who teach Properties of tangents
Top Tutor 
Virugambakkam, Chennai 
36 students 
1399 hrs of classes completed 
500 per hour 
Online Classes I am R.Vinotha ., M.Sc.,M.Phil.,B.Ed in mathematics.I am the trainer/tutor of this course .I was allotted 12 regular classes for a month.I am using through google meet app for online class and also i am taking mathematics tuition at my home.I will create seperate WhatApp group for my tuition students and communicates to them .I will send the class notes to them after completing the class .My class planner is us following: Regular classes : Any 3 days for a week Class duration : 1 hour Home works: Daily write two problems and send it to be in WhatsApp group Test: Daily test : Formulae test: Everyday i am asking 10 formulae through voice message in WhatsApp group after getting my message ,the students will answer the questions and send it tome via tuition group Problems test:Daily write two problems Regular test : Every saturday and sunday Monthly test : Every month fourth saturday doubts clarification time : Every day 7 pm -8 pm I will correct the test papers immedietly and send it to their personal windows and also resolve the students mistakes. Chapter's quiz : After completing every chapters ,i will conduct mathematical quiz for that chapters Revisions: I will revise previous years questio papers After this type of my coachings many of my students got 100 marks in theire board examination .I put lots of efforts to my students and they getting good marks in the board examination .My teaching type is friendly manner.I gave extra solved questions and answers to my students .
Taking class as well as gives coaching in different approaches that can be dealt with the topic thro variety in problems and helps to reach solution with clarity of the nuances to be careful with.
Top Tutor Sonari, Jamshedpur 4 students 657 hrs of classes completed 300 per hour Online Classes 
Student's Home 
Tutor's home I have a Science background completed my electrical engineering.... I am giving home tuition for 2 years.... I am also preparing for UPSC civil service exam.
Super Tutor Sector 5, Gurgaon 29 students 2318 hrs of classes completed 450 per hour Online Classes Tutor's home Mathematics is not just a subject—it is the backbone of science and the foundation for logical thinking and problem-solving. With over eleven years of teaching experience and a B.Tech degree, I am dedicated to nurturing students' mathematical abilities while instilling confidence and a love for learning. Recognitions & Achievements ✅ UrbanPro Excellency Awards – Top 10 in Class 10 Tuition (2024) & Top 100 Tutors for 2024 ✅ Teacher Innovation Award by ZIIEI (Sri Aurobindo Society) ✅ Certified by Leading Ed-Tech Platforms – UrbanPro Certification, GuruQ Certification These accolades reflect my commitment to providing high-quality education and delivering exceptional learning outcomes for my students. Why Choose Me as Your Child’s Tutor? As an educator, my primary goal is to empower students with a strong conceptual foundation while ensuring they enjoy the learning process. I believe that every child has unique strengths and learning needs, and my approach is tailored to bring out the best in them. 📌 Comprehensive Academic Support: I provide in-depth coaching in Mathematics, Science, and English for Grades V–X and specialize in Mathematics for Grades XI–XII and Undergraduate Courses. 📌 Expert in Competitive & Entrance Exam Preparation: I have successfully guided students in securing admissions to prestigious institutions and excelling in competitive exams, including: 🎯 School Entrance Exams – Sainik School, Military School, Navodaya Vidyalaya, Gurukul Entrance, Central Hindu School, Rai Sports School 🎯 Competitive & Government Job Exams – Olympiads, RIMC, NTSE, SSC MTS, CHSL, DSSSB 📌 Proven Track Record of Student Success: My students have consistently demonstrated remarkable improvement in grades and conceptual understanding. I maintain an individualized learning plan for each student, ensuring they receive personalized guidance and continuous support. Regular assessments, progress reports, and feedback sessions help track improvement and address learning gaps effectively. My Teaching Methodology & Approach I strongly believe that learning should be an engaging and interactive experience rather than rote memorization. My experiential learning approach is designed to: ✔ Encourage critical thinking and problem-solving skills ✔ Foster conceptual clarity through real-life applications ✔ Enhance creativity and independent learning To achieve this, I incorporate modern teaching tools and methodologies, such as: 🖥 Live Interactive Sessions – Engaging discussions to clarify doubts in real time 📊 PowerPoint Presentations & Animations – To visualize complex concepts easily 🖋 Whiteboard Teaching – Step-by-step breakdown of mathematical problems 📚 Comprehensive Study Materials, Worksheets & Assignments – Reinforcing learning through practice Online & Offline Classes: I conduct online classes via digital platforms and in-person sessions at my institute in Gurgaon. For students requiring additional support, I offer home tuition when feasible. Commitment to Student Success 🌟 Personalized Attention: I ensure that every student gets the individual focus they need to overcome challenges and master concepts. 🌟 Supportive Learning Environment: My classes are structured to be patient, encouraging, and motivating, allowing students to ask questions freely and develop confidence in their abilities. 🌟 Building Lifelong Skills: Beyond academics, I emphasize the development of problem-solving abilities, logical reasoning, and exam strategies that benefit students in their future careers. 🌟 Parental Involvement & Regular Feedback: I believe in open communication with parents to discuss their child’s progress, strengths, and areas for improvement. Regular performance reviews ensure that parents stay informed about their child's academic growth. Invest in Your Child’s Future Today! With a proven track record, structured teaching approach, and a passion for education, I am committed to helping students achieve excellence in Mathematics and beyond. If you are looking for a dedicated, award-winning tutor who can provide high-quality education, personalized guidance, and measurable results, I would be delighted to support your child’s learning journey. 📩 Contact me today to discuss how I can help your child excel!
Good techniques and enjoyed the class. Loved the way he explained things and gave tricks to save time as well.
Top Tutor MSR nagar mathikere, Bangalore 21 students 5691 hrs of classes completed 499 per hour Online Classes I enjoy teaching and making things easier and fun for the children. Didn't send my kids for any tuitions. Today the elder child is a CSE graduate , working for Amazon & the other is in her 3rd year MBBS !
I have been studying Maths and Science under her guidance since 8th grade. She explains every concept in a simple and clear way, making even difficult topics easy to understand. Her teaching style is patient and supportive, and she always makes sure all doubts are cleared. She focuses on strengthening basics and gives regular practice, which has really helped me improve. Because of her guidance, my confidence in both subjects has increased a lot. I am truly grateful for her dedication and support
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FAQ
What is the meaning of Properties of tangents?
It refers to a specific mathematical method or property in Circles used to solve problems involving Properties of tangents.
Why is Properties of tangents important for CBSE - Class 10 exams?
This concept is crucial for the exams as questions related to Circles and specifically Properties of tangents are very common. It helps secure marks in the section effectively.
Is Properties of tangents part of the latest NCERT syllabus?
Yes, Properties of tangents is an integral part of the CBSE - Class 10 NCERT Mathematics syllabus. It is a key topic covered in the Circles chapter.
What are common mistakes students make with Properties of tangents?
Students often miss the minute details or fundamental definitions of Properties of tangents. Regular revision and practice are needed to master the nuances.
How should I approach learning Properties of tangents?
Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.
How can UrbanPro help me understand Properties of tangents better?
UrbanPro connects you with experienced Mathematics tutors who can explain Properties of tangents with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.
