Question

if D IS THE MIDPOINT OF HYPOTENUSE AC OF RIGHT TRIANGLE ABC. PROVE THAT BD= 1/2 AC

Answer 1

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]

Answer 2

Take a right angled triangle ABC in which angle ABC=90° and AC=2a,AB=2b.AC=2√(a^2+b^2).A(0,2b),B(0,0) and C(2a,0).Mid point of AC is D(a,b).AD=√((a-0)^2+(b-0)^2)=√(a^2+b^2)=(1/2)AC.Hence AD=(1/2)AC.Hope this works……