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प्रश्न
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.
- Prove ΔPTB ~ ΔPAT
- Find the length of AB.
उत्तर
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
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