Question

13(a). In the diagram, lines |RS| and |RT| are tangent to the circle with centre O, ∠TUS=68°, ∠SRT=x° and ∠UTO=y°. Find the value of x°.
(b) Two tanks A and B are filled to capacity with diesel. Tank A holds 600 litres more diesel than tank B. If 100 litres of diesel was pumped out of each tank, tank A would then contain 3 times as much diesel as tank B. Find the capacity of each tank.

Accepted Answer

(a) OT and OS are radii of the circle, and ∠OTR = ∠OSR = 90° (radius meets tangent at 90°). ∠TOS = 2×∠TUS (angle at the centre is twice the angle at the circumference) = 2×68° = 136°. 
∠TOS+∠OTR+∠OSR+x° = 360° (sum of angles in a quadrilateral OTRS) ⇒ 136+90+90+x=360 ⇒ x° = 360−316 = 44°.

(b) Let a = capacity of tank A, b = capacity of tank B. a = b+600 …(i). After pumping out 100 litres from each: (a−100) = 3(b−100) …(ii). Substituting (i) into (ii): (b+600−100) = 3(b−100) ⇒ b+500 = 3b−300 ⇒ 500+300 = 3b−b ⇒ 800=2b ⇒ b=400 litres. From (i): a = 400+600 = 1000 litres.
Capacity of tank A = 1000 litres; capacity of tank B = 400 litres.

WAEC Mathematics 2019 Theory — Question 15

Sign up free to unlock