Theory question 103
Circle Theorems(a) In the diagram, ∠RTS = 28°, ∠VRM = 46°, MQ is a tangent to the circle VRSTU at the point R. Find ∠VUS.
(b) A cylindrical tin, 7 cm high, is closed at one end. If its total surface area is 462 cm2, calculate its radius. [Take π = 22/7]
Show the model answer
Model answer
(a) ∠VUR = ∠VRM = 46° (angle in the alternate segment)
∠RUS = ∠RTS = 28° (angles in the same segment)
∠VUS = 46° + 28° = 74°
(b) Total surface area = 2πrh + πr² = 462
22/7 × r(14 + r) = 462 → r² + 14r − 147 = 0 → (r − 7)(r + 21) = 0
r = 7 cm (r cannot be negative)
Explanation
Only one circular end is included because the tin is open at the other end.