Question
Download Solution PDFIn the figure, O is the centre of the circle. Its two chords AB and CD intersect each other at the point P within the circle. If AB = 20 cm, PB = 12 cm and CP = 8 cm, then find the measure of PD.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AB = 20 cm, PB = 12 cm and CP = 8 cm
Concept used:
If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.
AE × EC = DE × EB
Calculation:
According to the concept,
AP × PB = CP × PD
⇒ (AB - PB) × 12 = 8 × PD
⇒ (20 - 12) × 12 = 8 × PD
⇒ 8× 12 = 8 × PD
⇒ PD = 12
∴ The measure of PD is 12 cm.
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