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  • Two circles intersect at A and B, and through P, any point on the circumference of one of them, two straight lines PA and PB are drawn, and produced if necessary, to cut the other circle at x and y

Two circles intersect at A and B, and through P, any point on the circumference of one of them, two straight lines PA and PB are drawn, and produced if necessary, to cut the other circle at x and y. Find the locus of the intersection point of AY and BX.

Option: 1

Straight line 


Option: 2

parabola


Option: 3

ellipse


Option: 4

none of these


Answers (1)

best_answer

Let AY and BX intersect at R.

According to the figure\mathrm{\angle \mathrm{ARB}=\alpha+2 \beta=\text { constant }} 

for every position of P, \mathrm{\angle \mathrm{APB}=\alpha=\text { contt. }} and

\mathrm{\angle \mathrm{AXB}=\beta =\text { contt. }}∠AXB = β = contt.

⇒ locus of R is a circle making a fixed angle  

=\mathrm{\angle \mathrm{APB}+2 \angle \mathrm{AXB}} on the fixed chord AB.

 

Posted by

Gaurav

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