Problem
GEO-B2-M02-P004 Two Tangents
#4
★★☆☆☆ Level 2 of 5
From point \(P\), tangents \(PA\) and \(PB\) are drawn to a circle. Prove that \(PA=PB\) using power of a point.
The power of point \(P\) equals the square of any tangent from \(P\).
By the tangent formula, the power of point \(P\) with respect to the circle equals \(PA^2\). The same power also equals \(PB^2\). Therefore \(PA^2=PB^2\), and since lengths are positive, \(PA=PB\).
A familiar tangent property is reformulated in the language of power of a point.