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ICSE Class 10 Mathematics Question 15 of 21

Solved 2025 Specimen Paper ICSE Class 10 Mathematics — Question 8

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8
Question

Question 6(ii)

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.

(a) Prove △ PTB ~ △ PAT

(b) Find the length of AB.

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. ICSE 2025 Maths Solved Question Paper.
Answer

(a) In △ PTB and △ PAT,

⇒ ∠PTA = ∠PBT (Alternate segment theorem)

⇒ ∠TPA = ∠BPT (Common angle)

∴ △ PTB ~ △ PAT (By A.A. axiom)

Hence, proved that △ PTB ~ △ PAT.

(b) We know that,

If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.

⇒ PA × PB = PT2

⇒ PA × (PA + AB) = PT2

⇒ 16 × (16 + AB) = 202

⇒ 16 × (16 + AB) = 400

⇒ 16 + AB = 25

⇒ AB = 25 - 16 = 9 cm.

Hence, AB = 9 cm.