A triangle PQR is inscribed in a circle with its centre at O. A tangent PT is drawn at P such that \angle QPT = 36^\circ. What is \angle POQ equal to ?
- A. 36^\circ
- B. 54^\circ
- C. 72^\circ ✓
- D. 108^\circ
Correct Answer: C. 72^\circ
Explanation
By the Alternate Segment Theorem, the angle between the tangent and chord PQ equals the angle in the alternate segment, so \angle PRQ = 36^\circ. The angle subtended at the centre is twice the angle at the circumference, so \angle POQ = 2 \times 36^\circ = 72^\circ.
Related questions on Geometry
- In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
- ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
- The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
- An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
- The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...