Question

12(a). In the diagram, P, Q, R and S are points on the circle with centre O. ∠QOR=2m, ∠QPR=n and ∠SOR=54°. Find the values of m and n.
12(b). Let the width be W; the length is 4cm more than the width. If the perimeter is 40cm, find the area.

Accepted Answer

(a) ∠SOR=∠QRO=54° (alternate angles are equal, per the diagram's parallel lines). From triangle ORQ: 2m+54+54=180° → 2m=72° → m=36°. Also, ∠QOR(2m)=2×∠QPR(n) since the angle at the centre equals twice the angle at the circumference on the same arc: 2m=2n → m=n=36°.

(b) Let width=W, length=L=4+W. Perimeter=2(L+W)=40 → 2(4+W+W)=40 → 2(4+2W)=40 → 8+4W=40 → 4W=32 → W=8cm. Length=4+8=12cm. Area=L×W=12×8=96 cm².

WAEC Mathematics 2023 Theory — Question 12

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