Exam Questions & Step-by-Step Markschemes (51 Problems)
Question 1 • 2024
4 Marks
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
Answer: \angle APB + \angle AOB = 180^\circ \quad (AG)
Question 2 • 2023
4 Marks
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Answer: PQ = PR \text{ (Proved by RHS congruence)}
Question 3 • 2023
4 Marks
A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC .
Answer: AB + CD = AD + BC \quad (\text{Proved})
Question 4 • 2024
4 Marks
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Answer: \text{Hence Proved, } PQ = PR
Question 5 • 2024
5 Marks
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Answer: PQ = PR \quad \text{(Tangents are equal in length)}
Question 6 • 2025
1 Marks
Which of the following statements is false?
Answer: (B) Infinite number of tangents can be drawn to a circle from a point outside the circle.