Theory question 113
Circle Theorems(a) In the diagram, 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 of diesel more 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.
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Model answer
(a) ∠TOS = 2 × 68° = 136° (angle at centre)
∠OTR = ∠OSR = 90° (radius ⊥ tangent)
x = 360° − 90° − 90° − 136° = 44°
(b) Let B = x litres, A = x + 600
x + 600 − 100 = 3(x − 100) → x + 500 = 3x − 300 → x = 400
Tank B = 400 litres, Tank A = 1,000 litres
Explanation
In (a), the quadrilateral OTRS has two right angles where the tangents touch the circle.