✧Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6, find the radius of the circle.
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Answers
Answer:
Join OA and OC.
Let the radius of the circle be r cm and O be the centre
Draw OP⊥AB and OQ⊥CD.
We know, OQ⊥CD, OP⊥AB and AB∥CD.
Therefore, points P,O and Q are collinear. So, PQ=6 cm.
Let OP=x.
Then, OQ=(6–x) cm.
And OA=OC=r.
Also, AP=PB=2.5 cm and CQ=QD=5.5 cm.
(Perpendicular from the centre to a chord of the circle bisects the chord.)
In right triangles QAP and OCQ, we have
OA
2
=OP
2
+AP
2
and OC
2
=OQ
2
+CQ
2
∴r
2
=x
2
+(2.5)
2
..... (1)
and r
2
=(6−x)
2
+(5.5)
2
..... (2)
⇒x
2
+(2.5)
2
=(6−x)
2
+(5.5)
2
⇒x
2
+6.25=36−12x+x
2
+30.25
12x=60
∴x=5
Putting x=5 in (1), we get
r
2
=52+(2.5)
2
=25+6.25=31.25
⇒r
2
=31.25⇒r=5.6
Hence, the radius of the circle is 5.6 cm
Step-by-step explanation:
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