Question

4. In the given fig, if angle poq = 30°, then angle m =?​

Answer 1

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In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to

(A) 60° (B) 70° (C) 80° (D) 90°

In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to (A) 60° (B) 70° (C) 80° (D) 90°

Solution:

The tangent at any point of a circle is perpendicular to the radius at the point of contact.

In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to

In the above figure, OPTQ is a quadrilateral and ∠P and ∠Q are 90°

The sum of the interior angles of a quadrilateral is 360°.

Therefore, in OPTQ,

∠Q + ∠P + ∠POQ + ∠PTQ = 360°

90° + 90° + 110° + ∠PTQ = 360°

290° + ∠PTQ = 360°

∠PTQ = 360° - 290°

∠PTQ = 70°