Mathematics
In the given figure O is center, PQ is tangent at point A. BD is diameter and ∠AOD = 84° then angle QAD is :
32°
84°
48°
42°
Circles
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Answer
In △OAD,
OA = OD (Radius of same circle)
We know that,
Angles opposite to equal sides are equal.
∴ ∠A = ∠D = x (let)
⇒ ∠O + ∠A + ∠D = 180° (By angle sum property of triangle)
⇒ 84° + x + x = 180°
⇒ 2x = 180° - 84°
⇒ 2x = 96°
⇒ x = = 48°.
From figure,
∠OAD = ∠A = 48°
We know that,
Tangent at any point of a circle and the radius through this point are perpendicular to each other.
∴ ∠OAQ = 90°
From figure,
∠DAQ = ∠OAQ - ∠OAD = 90° - 48° = 42°.
Hence, Option 4 is the correct option.
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