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Question

# If the equal sides AB and AC (each equal to a) of a right angled isosceles △ABC be produced to P and Q so that BP⋅CQ=AB2, then the line PQ always passes through the fixed point.

A
(a,0)
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B
(0,a)
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C
(a,a)
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D
None of these
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Solution

## The correct option is D (a,a)We take A as the origin and AB and AC as x-axis and y-axis respectively.Let AP=h,AQ=kxh+yk=1⟶(1)Given BP.CQ=AB2⇒(h−a)(k−a)=a2 ⇒hk−ak−ah+a2=a2⇒hk−ak−ah+a2=a2ah+ak=1⟶(2)From (2) it follows that line (1), i.e PQ passes through the fixed point (a,a)

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