In the given figure, diameter AB of circle with centre O bisects the chord PQ. If PR = QR = 8 cm and RB = 4 cm, find the radius of the circle.
Answers
Answered by
2
Step-by-step explanation:
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,
OP
2
=OR
2
+PR
2
=>r
2
=(r−4)
2
+8
2
(using (i)
=>r
2
=r
2
−8r+16+64
=>8r=80
=>r=10cm
The radius of the circle is 10cm
Answered by
1
Answer:
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,
OP
2
=OR
2
+PR
2
=>r
2
=(r−4)
2
+8
2
(using (i)
=>r
2
=r
2
−8r+16+64
=>8r=80
=>r=10cm
The radius of the circle is 10cm
Similar questions