NumericalEasy1 mark
7(c)
In the given figure TP and TQ are two tangents to the circle with centre O, touching at A and C respectively. If ∠BCQ = 55° and ∠BAP = 60°, find :
∠ATC
Topic: Tangents / intersecting chords
Previous-year question practice database
Answer
Exam answer
From part (ii):
∠AOC = 130°
OA ⟂ TA and OC ⟂ TC
Therefore in quadrilateral AOTC:
∠OAT = 90° ∠OCT = 90°
Sum of angles of a quadrilateral = 360°.
So:
∠ATC = 360° − 90° − 90° − 130°
= 50°
Answer:
∠ATC = 50°.
Explanation
The radii OA and OC are perpendicular to the two tangents. Hence quadrilateral AOTC has two right angles, and the remaining two angles must sum to 180°.