Question : There are two circles which touch each other externally. The radius of the first circle with centre O is 17 cm and the radius of the second circle with centre A is 7 cm. BC is a direct common tangent to these two circles, where B and C are points on the circles with centres O and A, respectively. The length of BC is:
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution :
Since AB
AQBC is a rectangle with sides AQ = BC and AB = QC.
⇒ AP = AB = QC = 7 cm
and OC = OP = 17 cm
Also, AO = AP + PO = 7 +17 = 24 cm
and OQ = CO – CQ = 17 – 7 = 10 cm
In
AO
2
= AQ
2
+ OQ
2
⇒ 24
2
= AQ
2
+ 10
2
⇒ 576 = AQ
2
+ 100
⇒ AQ =
⇒ BC = AQ =
Hence, the correct answer is
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