CIR014 · Circles · Classes 9–11
Intersecting chords
When two chords cross at a point P inside a circle, the products of their parts are equal.
AP·PB = CP·PDIntersecting chords
📐 Formula
AP × PB = CP × PD = r² − OP²
✏️ Worked example
r = 4, OP = 2: for any chord through P, AP × PB = 16 − 4 = 12.
🌍 Where it is used
Finding the radius of an arch from measurements.
❓ Quick check
AP = 3, PB = 8, CP = 4. PD = ?
🏋️ Practice
EasyAP = 2, PB = 9, CP = 3. PD?
Answer: 6
MediumBoth chords are diameters. AP × PB?
Answer: r²
ChallengeAP = PB = 5 and CP = 2. PD?
Answer: 12.5