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In the adjoining figure P, Q and R the points of the circle, PT is the tangent to the circle at point P.

In the adjoining figure P, Q and R the points of the circle, PT is the tangent to the circle at point P. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Assertion (A): If ∠QPT = 50° and ∠PQR = 45°, then ∠QPR = 95°.

Reason (R): Angles in alternate segments are equal.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Circles

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Answer

According to alternate Segment theorem,

The angle between a tangent to a circle and a chord drawn from the point of contact is equal to the angle subtended by the chord in the alternate segment of the circle.

So, reason (R) is true.

∴ ∠QRP = ∠QPT (By alternate segment theorem)

⇒ ∠QRP = 50°

In ΔPQR, according to angle sum property,

∴ ∠PQR + ∠PRQ + ∠QPR = 180°

⇒ 45° + 50° + ∠QPR = 180°

⇒ 95° + ∠QPR = 180°

⇒ ∠QPR = 180° - 95°

⇒ ∠QPR = 85°

So, assertion (A) is false.

Thus, Assertion (A) is false, but Reason (R) is true.

Hence, option 2 is the correct option.

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