Find the best tutors and institutes for Class 10 Tuition
Learn Construction of tangents from external point
In CBSE Class 10 Mathematics, the "Constructions" chapter introduces students to precise geometric drafting. One of the most important and frequently tested concepts is the Construction of tangents from an external point to a given circle. A tangent is a straight line that touches the perimeter of a circle at exactly one point, known as the point of contact. Understanding how to accurately construct a pair of tangents from a point lying outside the circle is fundamental. It not only builds your spatial reasoning skills but also practically proves a key geometric theorem: exactly two tangents can be drawn to a circle from any external point, and the lengths of these two tangents are always equal.
The core logic behind this geometric construction relies on the foundational circle theorem that the angle in a semicircle is a right angle (90°). To construct the tangents, you must follow a series of logical steps: First, draw a circle with center O and a given radius, then mark the external point P. Join the points to create line segment OP. Next, construct the perpendicular bisector of OP to find its exact midpoint M. Using M as the new center and MO (or MP) as the radius, draw an auxiliary circle. The two points where this auxiliary circle intersects the original primary circle—let's name them A and B—are your exact points of contact. Finally, draw straight lines joining P to A, and P to B. Because the radii OA and OB are enclosed in the semicircles of the auxiliary circle, the angles ∠OAP and ∠OBP are strictly 90°. Since a line drawn perpendicular to a radius at the point of contact is a tangent, PA and PB are the required tangents.
By studying the diagram above, you can clearly visualize this step-by-step construction process. The primary circle (highlighted in blue) and the external point P form the foundation of our problem. By bisecting the line OP with the green dashed line, we discover the exact center M needed to draft our auxiliary circle (shown as a dashed grey ring). The magical intersection happens exactly at points A and B. Because these points lie on the circumference of the auxiliary circle whose diameter is OP, the triangles created—ΔOAP and ΔOBP—are perfect right-angled triangles. In CBSE board exams, questions on this topic often ask students to perform this construction manually using a compass and ruler, and then mathematically verify that the measured lengths of PA and PB are identical. Mastering this visual logic ensures full marks in your geometry practicals.
Geometry can sometimes feel overwhelming with its intricate steps, precise measurements, and underlying theorems. If you are finding Class 10 Math challenging, connecting with an experienced tutor can make a world of difference. On UrbanPro, you can easily find highly qualified and verified CBSE Class 10 Mathematics tutors who specialize in breaking down complex topics into easy-to-understand concepts. Whether you prefer personalized one-on-one online tutoring or focused local offline tuition classes, UrbanPro is India's most trusted learning network. Find your perfect tutor today and boost your board exam preparation with confidence!
Other Concept Videos for Construction of tangents from external point
Drawing Tangents to a Circle from Outside
CBSE - Class 10>Mathematics>Constructions>Construction of tangents from external point
Drawing Tangents to a Circle from Outside
CBSE - Class 10>Mathematics>Constructions>Construction of tangents from external point
Top Tutors who teach Construction of tangents from external point
Super Tutor 
Itagalpura Main Rd, Madappanahalli 
133 students 
3587 hrs of classes completed 
600 per hour 
Online Classes I gained extensive experience in delivering high-quality education following the CBSE/ICSE curriculum. My key responsibilities included: Classroom Teaching: Effectively taught Mathematics, Physics and Chemistry to students of classesX, ensuring alignment with the CBSE/ ICSE syllabus and fostering a deep understanding of key concepts. Curriculum Planning: Designed and implemented lesson plans that adhered to the CBSE guidelines, ensuring comprehensive coverage of topics while keeping in mind the varying learning needs of students. Student Assessment: Created and administered tests, quizzes, and assignments in accordance with the CBSE exam pattern. Monitored student performance and provided constructive feedback to facilitate continuous improvement. Interactive Learning: Encouraged an interactive classroom environment, integrating various teaching aids such as multimedia presentations, hands-on activities, and group discussions to enhance student engagement and understanding. Preparation for Board Exams: Provided focused support for students appearing for their CBSE/ICSE board exams by conducting regular revision sessions, mock tests, and personalized guidance to help them excel. Parental Communication: Maintained regular communication with parents regarding student progress, attendance, and overall development. Organized parent-teacher meetings to ensure a collaborative approach to student growth. Co-curricular Involvement: Actively participated in school events, projects, and extracurricular activities, fostering holistic development among students. Professional Development: Engaged in continuous professional development through workshops and CBSE training programs to stay updated with the latest educational practices and policies.
I have approached Sai sir for my daughter Maths tuition. The way you are interacting with student making learning so interesting and explaining everything was just outstanding. Your support and encouragement have given me the confidence.Thank you so much sir for your patience. Your teaching skills are very unique so that any student can easily grasp and enjoy learning.
Top Tutor Kharodi West, Mumbai 1 student 700 per hour 
Student's Home An accommodating and versatile individual with the talent to develop inspiring hands-on lessons that will capture a child's imagination and breed success.
Top Tutor Bavdhan Vidnyan Nagar, Pune 1 student 54 hrs of classes completed 250 per hour Online Classes 
Tutor's home I have taught in an institution to state ,ICSE , CBSE kids. Extra-ordinary Results. Ample of Study Material will be provided. We can have a demo class . You would enjoy the interactive and interesting sessions.
My experience with Parag sir was great, It is because of him that I got really good grades in my 10th and 12th standard.
Top Tutor Talwandi Sector-B, Kota 1 student 685 hrs of classes completed 1450 per hour Online Classes Tutor's home My teaching exp.11 year in most reputed coaching in india. Mentor of jee top rank air-12 yatis agrawal, 19, 28 many more in top 100 in jee adavnced. Many of students got 100%tile in jee mains along with 100% marks in board exams. I also provide complete relevent study material like worksheet, practice sheet , dpps , assignment etc. Daily quizz based on assignment. Periodically test papers topic wise, minor and major as per shedule. I have helped thousands of students overcome their fear of maths.
Top Tutor Bataganj, Patna Sadar 100 per hour Online Classes I am an experienced Spoken English and Class VI-X subject tutor with two years of experience in teaching. Currently, I am pursuing my bachelor's degree in BA from Magadh University. I can teach students who are in State, International Baccalaureate, CBSE and ICSE Board. My students have improved a lot through my teaching, and I've received five reviews till now with 100% positive feedback. I always try to understand my students and help them overcome their fear of failure in specific subjects like math and science.
Find more Tutor for Construction of tangents from external point in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Chandigarh Mathematics Tutors
- Surat Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
FAQ
What is the meaning of Construction of tangents from external point?
It refers to a specific mathematical method or property in Constructions used to solve problems involving Construction of tangents from external point.
Why is Construction of tangents from external point important for CBSE - Class 10 exams?
This concept is crucial for the exams as questions related to Constructions and specifically Construction of tangents from external point are very common. It helps secure marks in the section effectively.
Is Construction of tangents from external point part of the latest NCERT syllabus?
Yes, Construction of tangents from external point is an integral part of the CBSE - Class 10 NCERT Mathematics syllabus. It is a key topic covered in the Constructions chapter.
What are common mistakes students make with Construction of tangents from external point?
Students often miss the minute details or fundamental definitions of Construction of tangents from external point. Regular revision and practice are needed to master the nuances.
How should I approach learning Construction of tangents from external point?
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 Construction of tangents from external point better?
UrbanPro connects you with experienced Mathematics tutors who can explain Construction of tangents from external point with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.
