Question

If ∆ABC is isosceles with AB = AC and C (0, r) is the incircle of the ∆ABC touching BC at L. Prove that L bisects BC.

Answer 1

Given: In ∆ABC, AB = AC and a circle with centre O and radius r touches the side BC of ∆ABC at L.

Required to prove : L is mid-point of BC.

Proof :

AM and AN are the tangents to the circle from A.

So, AM = AN

But AB = AC (given)

AB – AN = AC – AM

⇒ BN = CM

Now BL and BN are the tangents from B

So, BL = BN

Similarly, CL and CM are tangents

CL = CM

But BN = CM (proved aboved)

So, BL = CL

Therefore, L is mid-point of BC.