if pQ and RS are two equal chords of a circle having its centre O. if ON= 3cm them OM=______ ?
Answers
Answered by
0
Answer:
Given, chords PQ=8 cm and RS=16 cm and AB=4 cm
Let perpendicular from the centre meet the chord RS at B and PQ at A.
Since, the perpendicular from the centre of the circle to the chord bisects the chord,
RB=BS=8 cm and PA=AQ=4 cm.
Let OB=x cm, then OA=OB+AB=(x+4) cm.
In right triangle OBS,
OS
2
=OB
2
+BS
2
=OB
2
+64 (i)
In right triangle OAQ,
OQ
2
=OA
2
+AQ
2
=OA
2
+16 (ii)
∴ OS and OQ are the radii of the circle
∴ OB
2
+64=OA
2
+16
⇒ x
2
+64=(x+4)
2
+16
⇒ x
2
+64=x
2
+8x+16+16
⇒ 8x=32⇒x=4
∴ From eqn (i)
Radius of the circle(OS)
2
=16+64=80
⇒ OS=4
5
cm
Similar questions