Problem
GEO-B2-M02-P015 Intersection of Diagonals in a Cyclic Quadrilateral
#15
★★★★☆ Level 4 of 5
In cyclic quadrilateral \(ABCD\), diagonals \(AC\) and \(BD\) meet at point \(P\). Prove that \(PA\cdot PC=PB\cdot PD\).
Consider point \(P\) as an interior point of the circle.
Diagonals \(AC\) and \(BD\) are chords of one circle and meet at \(P\). By the intersecting-chords theorem, \(PA\cdot PC=PB\cdot PD\).
A classical fact often needed in stronger problems.