Condition for Perpendicularity of Two Straight Lines
Let PQ and RS...
Question
Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals
A
PQ+RS2
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B
√PQ×RS
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C
2PQ×RSPQ+RS
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D
√(PQ2+RS2)2
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Solution
The correct option is B√PQ×RS
From the above figure, we have PQPR=tan(π2−θ)=cotθ
and RSPR=tanθ ⇒PQPR.RSPR=1 ⇒(PR)2=PQ.RS ⇒(2r)2=PQ.RS ⇒2r=√PQ.RS