Mathematics
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 :
x
180° - 2x
90° + x
90° - x
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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