Exam Questions & Step-by-Step Markschemes (3 Problems)
Question 1 • 2024
4 Marks
In the given figure, PT is a tangent to the circle drawn from an external point P , touching the circle at T . A straight secant line through P intersects the circle at points A and B (with A lying between P and B ). If PT = 8\text{ cm} and PA = 4\text{ cm} , calculate: (i) The length of the entire secant segment PB . (ii) The length of the chord AB .
Answer: (i) \; PB = 16\text{ cm}, \quad (ii) \; AB = 12\text{ cm}
Question 2 • 2023
4 Marks
In a circle with center O , AB is a diameter and AC is a chord such that \angle BAC = 30^\circ . The tangent at C intersects AB produced at D . Find: (i) \angle BCD (ii) \angle ADC
Answer: (i) \ \angle BCD = 30^\circ \quad (ii) \ \angle ADC = 30^\circ
Question 3 • 2023
4 Marks
In the given circle, chords AB and CD intersect internally at P . If AP = 8\text{ cm}, PB = 3\text{ cm} and CP = 4\text{ cm} , find PD . If PT is a tangent drawn from an external point P' on secant P'AB such that P'A = 4\text{ cm} and AB = 5\text{ cm} , find the length of tangent P'T .
Answer: PD = 6\text{ cm}, \quad P'T = 6\text{ cm}