Problem
GEO-B2-M02-P019 Equal Tangents to Two Circles
#19
★★★★☆ Level 4 of 5
From point \(P\), tangents \(PT_1\) and \(PT_2\) are drawn to two circles. Prove that if \(PT_1=PT_2\), then the powers of point \(P\) with respect to these circles are equal.
The power equals the square of the tangent.
The power of point \(P\) with respect to the first circle equals \(PT_1^2\), and with respect to the second equals \(PT_2^2\). If \(PT_1=PT_2\), then \(PT_1^2=PT_2^2\). Therefore the powers are equal.
A short exercise in the language of equal powers before the radical axis.