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Two chords AB and CD intersect at a point P inside a circle. If AP = 6 cm, PB = 8 cm, and CP = 4 cm, what is the length of PD?
Question

Two chords AB and CD intersect at a point P inside a circle. If AP = 6 cm, PB = 8 cm, and CP = 4 cm, what is the length of PD?

A.

10 cm

B.

12 cm

C.

16 cm

D.

18 cm

Correct option is B

Given :

Two chords AB and CD intersect at point P inside a circle.
AP = 6 cm, PB = 8 cm, CP = 4cm
Length of PD = ?

Formula Used :
Intersecting chords theorem:
AP×PB=CP×PDP \times PB = CP \times PD​​

Solution :

6×8=4×PD6 \times 8 = 4 \times PD​​

48 = 4×4 \times ​PD

PD = 12 cm

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