Question
Download Solution PDFThere are two circles which touch each other externally. The radius of the first circle with centre O is 17 cm and 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of first circle = 17 cm
Radius of second circle = 7 cm
Circles touch each other externally.
BC is a direct common tangent of these two circles.
Concept used:
External tangents are lines that do not cross the segment joining the centers of the circles.
Calculation:
Join A to O and B. Join O to C. Draw AQ perpendicular to OC.
Now, AQ = BC, as they are opposite sides of rectangle AQCB.
⇒AO = AP + PQ
⇒AO = 7 + 17
⇒AO = 24 cm
⇒OQ = CO - CQ
⇒OQ = 17 - 7
⇒OQ = 10 cm
Now, applying pythagoras theorem in triangle AOQ:
⇒
⇒AQ =
⇒AQ =
⇒AQ =
∴ The length of BC is
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