<p>\(AC\) and \(BD\) are chords of a circle with radius \(r\). \(AC\), \(BD\) intersect at \(P\) and \(AC \perp BD\), show that&nbsp;\(AP^2 + BP^2 + CP^2 + DP^2 = 4r^2\).</p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1775801930527-9nlbpx4xiue.png" style="max-width: min(220px, 100%); height: auto; display: block;" alt="A circle with center \(O\) and two perpendicular chords \(AC\) and \(BD\) intersecting at point \(P\)." class="alignright custom-width" /></figure></div>

\(AC\) and \(BD\) are chords of a circle with radius \(r\). \(AC\), \(BD\) intersect at \(P\) and \(AC \perp BD\), show that \(AP^2 + BP^2 + CP^2 + DP^2 = 4r^2\).

Property of Perpendicular Chords

Property of Perpendicular Chords