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Question
If two tangents TL and TM are drawn to a circle with centre C such that ∠LTM = 70°, then find ∠MCT.
Options
30°
60°
45°
55°
Solution
55°
Explanation:
In the given figure, TC bisects ∠LTM.
∴ ∠CTM = `1/2` ∠LTM
= `1/2` × 70°
= 35°
Also, ∠CMT = 90° ......[Tangent theorem]
In ΔTCM,
∠MCT + ∠CMT + ∠CTM = 180°
∠MCT + 90° + 35° = 180°
∠MCT = 180° – 90° – 35° = 55°
Thus, ∠MCT = 55°.
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