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Question
In the following figure, ray PA is a tangent to the circle at A and PBC is a secant. If AP = 15, BP = 10, then find BC.
Solution
In the given figure, PA is a tangent segment and PBC is the secant
∴ PB x PC = PA2
`:. 10 xx PC = 15^2`
`:. PC = 225/10 = 22.5`
NOw PB + BC = PC .............(P - B - C)
∴ 10 + BC = 22.5
∴ BC = 22.5 - 10 = 12.5
Therefore BC = 12.5
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RELATED QUESTIONS
In the following figure, a tangent segment PA touching a circle in A and a secant PBC is shown. If AP = 15, BP = 10, find BC.
In the given figure, P is the point of contact.
(1) If m(arc PR) = 140°, ∠ POR = 36°, find m(arc PQ)
(2) If OP = 7.2, OQ = 3.2, find OR and QR
(3) If OP = 7.2, OR = 16.2, find QR.
In the figure given above, ‘O’ is the centre of the circle, seg PS is a tangent segment and S is the point of contact. Line PR is a secant.
If PQ = 3.6, QR = 6.4, find PS.
Solution:
PS2 = PQ × `square` ......(tangent secant segments theorem)
= PQ × (PQ + `square`)
= 3.6 × (3.6 + 6.4)
= 3.6 × `square`
= 36
∴ PS = `square` .....(by taking square roots)
