ABC is a triangle in which AB = AC and D is any point in BC. Prove that : (AB)2 – (AD)2 = BD . CD.

Asked by Last Modified  

1 Answer

Learn Mathematics +1 Class IX-X Tuition

Follow 1
Answer

Please enter your answer

Learner

Draw the perpendicular from A to BC. Let it intersect BC at E. Then in triangle AEB we have: AB^2 = AE^2 + BE^2 In triangle AED we have: AD^2 = AE^2 + BD^2 Subtracting gives: AB^2 - AD^2 = BE^2 - BD^2 AB^2 - AD^2 = (BE + BD)(BE - BD) Now, the perpendicular to the unequal side in an isosceles...
read more
Draw the perpendicular from A to BC. Let it intersect BC at E. Then in triangle AEB we have: AB^2 = AE^2 + BE^2 In triangle AED we have: AD^2 = AE^2 + BD^2 Subtracting gives: AB^2 - AD^2 = BE^2 - BD^2 AB^2 - AD^2 = (BE + BD)(BE - BD) Now, the perpendicular to the unequal side in an isosceles triangle is also the bisector of the unequal side. This can be proved by considering triangles AEB and AEC AB = AC angle AEB = angle AEC AE = AE By RHS criterion, the two triangles are congruent. So BE = CE Depending on where you draw point E, you can get one of two things: BE + ED = BD and BE - ED = CE - ED = CD (or) BE + ED = CE + ED = CD and BE - ED = BD In either case you get: (BE+ED)*(BE-ED) = BD*CD. Thus: AB^2 - AD^2 = BD*CD read less
Comments
Dislike Bookmark

Related Questions

What was your experience in Class X? Do you think the board exams are really that hard?
No, actually if you study really wel keeping in mind each and every aspect, then 10th boards are really not that hard. Stay focused , practice alot and work hard.
Sanjeevani
0 0
View Comments8
What should I do to pass class 10?
You focus on subjects which are difficult for you.do not target big,just target to pass subjects which are difficult.Just focus on main topics.
Pankaj
0 0
View Comments6
Is linear algebra a hard class? Why or why not?
It is very easy ,but it takes time to solve and simply the equation.
Subhasish
0 0
View Comments6
If x:y = 9:10, find the value of (5x + 3y) : (5x - 3y)?
(5x + 3y) : (5x - 3y)=(5x/y+3):(5x/y-3) =(5*9/10+3):(5*9/10-3) =15/3=5
Altaf
What is the three rational numbers lying between 1/3 and 1/2?
Three rational numbers between 1/3 and 1/2 making the denominator same: 1/3=8/24(equivalent fraction) 1/2=12/24(also equivalent fraction). Three rational numbers between 8/24 and 12/24 are: 9/24,10/24,11/24.
Avinash

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Cordinate Axis retangular to polar and polar to rectangular Conversion
The system of coordinates is known as the Cartesian System of Coordinates. It is so called because this system was first introduced by the philosopher Des Cartes. There are other systems of coordinates...

Raj Kumar

0 0
View Comments0
Class-10 L-1 Real Numbers Ex-1.1 Q3 (i)

Ashish Bhatia

0 0
View Comments0
Class-10 L-5 Arithmetic Progressions Ex-5.2 Q1 (iii)

Ashish Bhatia

0 0
View Comments0
Class-10 L-5 Arithmetic Progressions Ex-5.1 Q4 (i)-(iv)

Ashish Bhatia

0 0
View Comments0
Master Euclid’s Division Lemma with Simple Steps

Saurav

0 0
View Comments0

Recommended Articles

Meet Sandhya R, a B.Sc tutor from Bangalore

Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...

Read full article >

Meet Raghunandan.G.H, a B. Tech Tutor from...

Raghunandan is a passionate teacher with a decade of teaching experience. Being a skilled trainer with extensive knowledge, he provides high-quality BTech, Class 10 and Class 12 tuition classes. His methods of teaching with real-time examples makes difficult topics simple to understand. He explains every concept in-detail...

Read full article >

Quest Academy - Institute of the month

Quest Academy is a professional Bangalore based NEET and JEE (Main + Advanced) training institute. The academy was incorporated in 2015 to cater to the needs of students, who aim to crack competitive exams by connecting with the best brains around. The institute helps students enhance their skills and capabilities through...

Read full article >

Meet Mohammad Wazid, a skilled trainer for...

Mohammad Wazid is a certified professional tutor for class 11 students. He has 6 years of teaching experience which he couples with an energetic attitude and a vision of making any subject easy for the students. Over the years he has developed skills with a capability of understanding the requirements of the students. This...

Read full article >

Find Class 10 Tuition near you
Class 10 Tuition in Delhi
Class 10 Tuition in Bangalore
Class 10 Tuition in Hyderabad
Class 10 Tuition in Kolkata
Class 10 Tuition in Mumbai
Class 10 Tuition in Chennai
Class 10 Tuition in Pune
Class 10 Tuition in Lucknow
Class 10 Tuition in Noida
Class 10 Tuition in Jaipur
Online Tuition Class 10

Looking for Class 10 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you