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JAMB Mathematics 2023 Paper

Question : 10

Total: 80

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Solution:

From ∆PSR

|PS| = |SR| (If two tangents are drawn from an external point of the circle, then they are of equal lengths)

∴ ∆PSR is isosceles

∠PSR + ∠SRP + ∠SPR = 180

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(sum of angles in a triangle)

Since |PS| = |SR|; ∠SRP = ∠SPR

⇒ ∠PSR + ∠SRP + ∠SRP = 180

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∠PSR + 2∠SRP = 180

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+ 2∠SRP = 180

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2∠SRP = 180

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- 36

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2∠SRP = 144

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∠SRP = $\frac{144^{\circ}}{2} = 72^{\circ}$

∠SRP = ∠PQR (angle formed by a tangent and chord is equal to the angle in the alternate segment)

∴ ∠PQR = 72

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