Question

7(a) Using completing the squares method, solve, correct to 2 decimal places: (x-2)/4 = (x+2)/2x
(b) In the diagram above, PQRST is a circle with centre O. If PS is a diameter, RS//QT, |RS| and ∠QTS=52°, find: (i) ∠SQT (ii) ∠PQT

Accepted Answer

(a) (x-2)/4 = (x+2)/2x
Cross multiply: (x-2)(2x) = 4(x+2)
2x²-4x = 4x+8
2x²-8x-8=0
x²-4x-4=0
Completing the square: (x-2)²=4+4=8
x-2=±√8
x=2±2.83
x=4.83 or x=-0.83 (2 d.p.)

(b)(i) ∠SQT = ∠STQ... Using the circle theorem, since RS//QT and ∠QTS=52°, ∠SQT=52° (alternate angles, since RS//QT means ∠RST=∠QTS, and by alternate segment theorem applied within the circle, ∠SQT=52°).
(ii) Since PS is a diameter, ∠PQS=90° (angle in semicircle). ∠PQT=∠PQS-∠SQT=90°-52°=38°.

WAEC Mathematics 2016 Theory — Question 7

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