PQ perpendicular OQ. The tangent to …
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Naveen Sharma 7 years, 3 months ago
Ans.
Given: AP and AQ are tangents to the circle with centre O, AP ⊥ AQ and AP = AQ = 5 cm
we know that radius of a circle is perpendicular to the tangent at the point of contact
⇒ OP ⊥ AP and OQ ⊥ AQ
Also sum of all angles of a quadrilateral is 360° ⇒∠O + ∠P + ∠A + ∠Q = 360°
⇒∠O + 90° + 90° + 90° = 360°
⇒∠O = 360° – 270° = 90°
Thus ∠O = ∠P = ∠A = ∠Q = 90°
⇒ OPAQ is a rectangle but since adjacent sides of OPAQ i.e. AP and AQ are equal.
Thus OPAQ is a square
radius = OP = OQ = AP = AQ = 5 cm
Since diagonals of a square are perpendicular bisector of each other.
Hence PQ and OA are perpendicular bisectors of each other
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