10 questions · Form 3 Mathematics Bab 6: Angles and Tangents of Circles
Points P, Q, and R lie on a circle with centre O. If reflex angle POR = 240°, what is the acute/obtuse angle PQR at the circumference?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Points P, Q, and R lie on a circle with centre O. If reflex angle POR = 240°, what is the acute/obtuse angle PQR at the circumference?
Answer: A
The subtended angle at circumference = Reflex angle at centre2 = 240° / 2 = 120°.
2. What is the angle formed between a tangent line and the radius drawn to the point of contact?
Answer: C
A tangent to a circle is always perpendicular (90°) to the radius at the point of contact.
3. In a circle, chords AB and CD intersect. If PQ represents a tangent at P and chord PR makes an angle of 52° with tangent PQ, what is the angle subtended by chord PR in the alternate segment?
Answer: A
By the Alternate Segment Theorem, the angle in the alternate segment equals the angle between the tangent and chord, which is 52°.
4. Two tangents from an external point T touch a circle at P and Q. If angle PTQ = 40°, what is angle POQ at the centre of the circle?
Answer: A
Quadrilateral OPTQ has right angles at P and Q (90° each). Thus, angle POQ + angle PTQ = 180° => POQ = 180° - 40° = 140°.
5. In a circle with centre O, PT is a tangent to the circle at point P. If OP = 5 cm and OT = 13 cm, calculate the length of tangent PT.
Answer: A
Triangle OPT is right-angled at P. PT = √(13² - 5²) = √(169 - 25) = √144 = 12 cm.
6. In a right-angled triangle formed inside a semicircle with the diameter as its hypotenuse, if one acute angle is 35°, what is the other acute angle?
Answer: A
The angle in the semicircle is 90°. The sum of angles in a triangle is 180°, so the third angle = 180° - 90° - 35° = 55°.
7. What is the sum of opposite interior angles in a cyclic quadrilateral?
Answer: B
Opposite interior angles in a cyclic quadrilateral are supplementary, meaning their sum is 180°.
8. In a cyclic quadrilateral ABCD, if angle A = 75°, what is the measure of its opposite angle C?
Answer: B
Angle C = 180° - 75° = 105°.
9. The exterior angle of a cyclic quadrilateral is always equal to:
Answer: B
The exterior angle formed by extending one side of a cyclic quadrilateral is equal to the interior opposite angle.
10. If arc AB subtends an angle of 40° at the circumference, what is the angle subtended by arc AB at the centre?
Answer: C
Angle at centre = 2 × Angle at circumference = 2 × 40° = 80°.