JEE Advance - Mathematics (1998 - No. 49)
$$C_1$$ and $$C_2$$ are two concentric circles, the radius of $$C_2$$ being twice that of $$C_1$$. From a point P on $$C_2$$, tangents PA and PB are drawn to $$C_1$$. Prove that the centroid of the triangle PAB lies on $$C_1$$.
Let O be the center of the concentric circles.
Let the radius of $$C_1$$ be r, then the radius of $$C_2$$ is 2r.
Since PA and PB are tangents to $$C_1$$, $$OA \perp PA$$ and $$OB \perp PB$$.
Let M be the midpoint of AB, then $$PM \perp AB$$.
The centroid lies on C1.
Comments (0)
