The adjoining figure shows a circle with centre O in which a diameter AB bisects the chord PQ at point R. If PR=RQ=8 cm and RB=4 cm, find the radius of the circle.
10 cm
12 cm
16 cm
8 cm
A
10 cm
B
16 cm
C
8 cm
D
12 cm
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Solution
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AB bisects chord PQ at point C. Therefore, PR=QR=8cm RB=4cm Let, radius OA=OB=r OB=OR+RB =>r=OR+4 =>OR=r−4 (i) Now, OP2=OR2+PR2 =>r2=(r−4)2+82 (using (i) =>r2=r2−8r+16+64 =>8r=80 =>r=10cm The radius of the circle is 10cm
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