A geometry problem by Parth Sankhe

Geometry Level pending

There is a circle with centre at $(2,-3)$ and radius = $4$ . There is a point $P(7,1)$ on the exterior of the circle.

Find the equation of the line which bisects the tangents from $P$ to the circle.

If the line can be expressed in the form $ax+by-c=0$ where a,b,c are positive coprime integers, find the value of $a+b+c$ .

The answer is 71.

1 solution

Parth Sankhe
Oct 28, 2018

Assume P to be a point circle and write its equation assuming its radius to be 0. Accordingly, the line asked for becomes the radical axis of the 2 circles. Equate their equations $S_1=0$ and $S_2=0$ to give the radical axis, and thus the answer. $L\rightarrow 10x+8y=53$

A geometry problem by Parth Sankhe

The answer is 71.

1 solution

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