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In the given figure, O is center of the circle and PQ is a tangent. If angle OAB = x; the measure of angle ABP; in terms of x, is :

  1. x

  2. 180° - 2x

  3. 90° + x

  4. 90° - x

In the given figure, O is center of the circle and PQ is a tangent. If angle OAB = x; the measure of angle ABP; in terms of x, is : Tangents and Intersecting Chords, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

From figure,

In △OAB,

OA = OB (Radius of same circle)

We know that,

Angles opposite to equal sides are equal.

⇒ ∠OBA = ∠OAB = x

We know that,

Tangent at any point of a circle and the radius through this point are perpendicular to each other.

∴ OB ⊥ PQ

∴ ∠PBO = 90°

From figure,

∠ABP = ∠PBO - ∠OBA = 90° - x.

Hence, Option 4 is the correct option.

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