Problem
GEO-B2-M03-P017 A Point on the Radical Axis and Tangents
#17
★★★★☆ Level 4 of 5
Point \(P\) lies on the radical axis of two circles and is outside both circles. Tangents \(PT_1\) and \(PT_2\) are drawn from \(P\) to them. Prove that \(PT_1=PT_2\).
The powers are equal, and each power equals the square of the tangent.
Since \(P\) lies on the radical axis, the powers of point \(P\) with respect to the two circles are equal. But these powers are \(PT_1^2\) and \(PT_2^2\). Hence \(PT_1^2=PT_2^2\), and since lengths are positive, \(PT_1=PT_2\).
The reverse direction of the equal tangents problem.