Question : If PQ is a tangent of a circle (touches the circle at Q ) with centre O and angle POQ is 75°, then what is the value of angle OPQ?
Option 1: 15°
Option 2: 35°
Option 3: 30°
Option 4: 25°
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Correct Answer: 15°
Solution : In a circle, the radius is perpendicular to the tangent at the point of tangency. This means the angle between the radius (OQ) and the tangent (PQ) is 90°. Given that the $\angle$POQ is 75°, $\angle$OPQ = 180° – 90° – 75° = 15° Hence, the correct answer is 15°.
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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 : 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 4: 45°
Question : ST is a tangent to the circle at P and QR is the diameter of the circle. If $\angle$RPT = 50°. Then the value of $\angle$SPQ is:
Option 1: 40°
Option 3: 80°
Option 4: 100°
Question : Points D, E, and F all lie on the circumference of a circle with centre O. If angle DEF = 48°, then what is a possible value of angle DOF?
Option 1: 84°
Option 2: 96°
Option 4: 48°
Question : AB is a chord of the circle and AOC is its diameter such that $\angle$ACB = 65°. If AT is the tangent to the circle at the point A, then $\angle$BAT is equal to:
Option 1: 65°
Option 2: 75°
Option 3: 55°
Option 4: 40°
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