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°

Answer 1

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°.