Two circles of radio 18 cm and 8 cm touches externally.find the length of a direct common tangent to the two circles.
Answers
The length of a direct common tangent to the two circles is 24 cm.
Step-by-step explanation:
=> Here, Two circles of radio 18 cm and 8 cm touches externally.
Thus, Radius of first circle, R = 18 cm
Radius of second circle, r = 8 cm
=> Distance between the centres of two circle:
d(oo') = R + r
= 18 + 8
= 26 cm
=> So, the length of a direct common tangent to the two circles:
l = √d² - (R - r)²
= √ 26² - (18 - 8)²
= √ 26² - 10²
= √ 676 - 100
= √ 576
= 24 cm
Thus, the length of a direct common tangent to the two circles is 24 cm.
Learn more:
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Q:2 Two circles with centres o and o' of radius 3cm and 4cm respectively intersect at two points p and q such that op and op are tangents to the two circles. find the length of the common chord pq.
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Answer:Two circles of radio 18 cm and 8 cm touches externally.
Thus, Radius of first circle, R = 18 cm
Radius of second circle, r = 8 cm
=> Distance between the centres of two circle:
d(oo') = R + r
= 18 + 8
= 26 cm
=> So, the length of a direct common tangent to the two circles:
l = √d² - (R - r)²
= √ 26² - (18 - 8)²
= √ 26² - 10²
= √ 676 - 100
= √ 576
= 24 cm Ans...
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Step-by-step explanation: