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Question
In the given figure, PQ and PR are tangents to a circle centred at O. If ∠QPR = 35° then ∠QOR is equal to ________.
Options
70°
90°
135°
145°
MCQ
Fill in the Blanks
Solution
In the given figure, PQ and PR are tangents to a circle centred at O. If ∠QPR = 35° then ∠QOR is equal to 145°.
Explanation:
Given, ∠QPR = 35°
PQ and PR are tangents.
Therefore, the radius drawn to these tangents will be perpendicular to the tangents.
So, we have OQ ⊥ PQ and OR ⊥ PR
⇒ ∠OQP = ∠ORP = 90°
So, in quadrilateral PQOR, we have
∠OQP + ∠ORP + ∠QPR + ∠QOR = 360°
215° + ∠QOR = 360°
∠QOR = 360° − 215°
= 145°
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