Consider a circle C1 with equation (x−1)2+y2=1 and a shrinking circle C2 with radius r and centre at the origin. P is the point (0,r), Q is the point of intersection of the two circles(above x-axis) and R is the point of intersection of the line PQ with the x-axis. Find the x-coordinate of the point R, as C2 shrinks, that is r→0.

Consider a circle C1 with equation (x−1)2+y2=1 and a shrinking circl

1.	Consider a circle C1 with equation (x−1)2+y2=1 and a shrinking circle C2 with radius r and centre at the origin. P is the point (0,r), Q is the point of intersection of the two circles(above x-axis) and R is the point of intersection of the line PQ with the x-axis. Find the x-coordinate of the point R, as C2 shrinks, that is r→0.
Answer» Consider a circle $C_{1}$ with equation $(x - 1)^{2} + y^{2} = 1$ and a shrinking circle $C_{2}$ with radius $r$ and centre at the origin. $P$ is the point $(0, r), Q$ is the point of intersection of the two circles(above x-axis) and $R$ is the point of intersection of the line $P Q$ with the x-axis. Find the x-coordinate of the point $R,$ as $C_{2}$ shrinks, that is $r \to 0$ .