Question

If D is a mid-point of the hypotenuse AC of a right angled triangle ABC ( right angled at B ), prove that BD=1/2 AC

Answer 1

Answer:

GIVEN: A right triangle ABC, right angled at B. D is the mid point of AC, ie, AD = CD

TO PROVE : BD = AC/2

Since, circumcentre of any right triangle is the mid point of its hypotenuse.

=> D is the centre of the circle passing through A, B & C

=> AD = BD = CD ( being radii of the same circle)

Or 2AD = 2BD

=> AC = 2BD

=> BD = AC/2

[Hence Proved]

Hope it helps!!