Question

If ABC is a right angled triangle Such that AB=AC and bisector of angle C intersects the side AB at D. Then Prove that AC+AD=BC.

Answer 1

Answer:

let AC = x

then BC = 2–√ x

as AD and DB will be in ratio of AC and BC by angle bisector theorem

so let AD = y and so DB = 2–√ y

but AD + DB = AB = AC

so y+ 2–√ y = x

y( 2–√ + 1) = x

so y = x2–√+1

on rationalising the denominator it results in

y = ( 2–√ - 1) x

add x on both sides

y + x= ( 2–√ - 1) x + x

AD + AC = ( 2–√ - 1 + 1) x

AD + AC = ( 2–√ ) x

so AC + AD = BC

Alternatively it becomes very easy if you know how to calculate

trignometric ratios for 22.5 deg

then AD/AC is just tan(22.5deg) and you can very easily get things done from there.

Hope it suits u✌✌✌