Question

In the given figure PT is a tangent to the circle. Chord BA produced meets the tangent PT at P.

Given PT = 20 cm and PA = 16 cm.

1. Prove ΔPTB ~ ΔPAT
2. Find the length of AB.

Answer 1

a. In ΔPTB and ΔPAT,

∠ PTA = ∠PBT  ...(Alternate segment theorem)

∠TPA = ∠BPT  ...(Common ∠)

∴ ΔPTB ~ ΔPAT  ...(AA axiom)

b. PA × PB = PT²

`\implies` 16(16 + AB) = 400

`\implies` 16 + AB = 25

`\implies` AB = 9 cm