Question : In a circle if PQ is the diameter of the circle and R is on the circumference of the circle such that $\angle$PQR = 30°, then $\angle$RPQ =?
Option 1: 90°
Option 2: 60°
Option 3: 30°
Option 4: 45°
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Correct Answer: 60°
Solution : Given: $\angle$PQR = 30° We know the angle of a semi-circle is a right angle, so $\angle$PRQ = 90° So, $\angle$RPQ = 180° – $\angle$PQR – $\angle$PRQ = 180° – 30° – 90° = 60° Hence, the correct answer is 60°.
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Question : AC is the diameter of the circle. B is a point on the circumference. If $\angle$BAC is 40°, then what is $\angle$BCA?
Option 1: 50°
Option 2: 90°
Option 3: 55°
Option 4: 40°
Question : A, B, P, and Q are points on the circumference of a circle with centre O. If angle AQB is 60°, then which of the following can be the value of angle APB?
Option 1: 160°
Option 2: 30°
Option 3: 90°
Option 4: 60°
Question : From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to the diameter of the circle, then $\angle$APB is:
Option 1: 45°
Question : AB is the diameter of a circle with centre O. P is a point on it. If $\angle$POA = 120°. Then $\angle$PBO = ?
Option 1: 60°
Option 2: 120°
Option 3: 45°
Option 4: 50°
Question : The angle subtended by a chord on the centre of a circle is 180°. What will be the angle subtended by the same chord on the circumference of this circle?
Option 1: 120°
Option 2: 95°
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