help@askiitians.com

+91-705-589-3577

9 grade maths> In a Triangle ABC, angle A = 90 0 , CA=AB...

question mark

In a Triangle ABC, angle A = 90⁰, CA=AB,
D is a point on BC produced. Prove that AD²=AC²+BD X CD

Dipankar Ghosh , 11 Years ago

Grade 9

1 Answers

Sumit Majumdar

From the figure, we see that:
$AD^2=AE^2+ED^2=\left(AC+CE \right )^2+ED^2=AC^2+CE^2+AC\cdot CE+ED^2$
From symmetry of triangles, we know that
$AC\cdot CE=BC\cdot CD$
So, we get
$AD^2=AC^2+CE^2+BC\cdot CD+ED^2=AC^2+BC\cdot CD+CD^2=AC^2+BC\left(BC+CD \right )=AC^2+BD\cdot CD$

Last Activity: 10 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

What are the differences between similar triangles and congruent triangles?

9 grade maths

1 Answer Available

Last Activity: 7 Months ago

What are Armstrong numbers?

9 grade maths

1 Answer Available

Last Activity: 7 Months ago

All real numbers are rational numbers.
A) True
B) False

9 grade maths

1 Answer Available

Last Activity: 7 Months ago

The L.C.M of the smallest 2 digit composite number and the smallest composite number is:
(a) 12
(b) 4
(c) 20
(d) 44

9 grade maths

1 Answer Available

Last Activity: 7 Months ago

Are all natural numbers also whole numbers?

9 grade maths

1 Answer Available

Last Activity: 7 Months ago

View all Questions