JAMB Mathematics 2023 Paper

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 = 180‌o (sum of angles in a triangle)

Since |PS| = |SR|; ∠SRP = ∠SPR

⇒ ∠PSR + ∠SRP + ∠SRP = 180‌o

∠PSR + 2∠SRP = 180‌o

36‌o + 2∠SRP = 180‌o

2∠SRP = 180‌o - 36‌o

2∠SRP = 144‌o

∠SRP =

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

∴ ∠PQR = 72‌0