Question

If ΔABC is isosceles with AB = AC and C (0, 2) is the in circle of the ΔABC touching BC at L, prove that L, bisects BC.

Answer 1

Given ΔABC is isosceles AB = AC

We know that

The tangents from external point to circle are equal in length

From point A, AP = AQ

But AB = AC ⇒ AP + PB = AQ + QC

⇒ PB = PC …. (i)

From B, PB = BL; ….(ii)        from C, CL = CQ …..(iii)

From (i), (ii) & (iii)

BL = CL

∴ L bisects BC.