Two circles of radii 10 cm and 8 cm

Asked by admin @ 17/08/2021 in Math viewed by 333 People

two circles of a radii 10cm and 8cm intersect and the length of the common chord is 12cm. find the distance between the centers

Answered by admin @ 17/08/2021

Center of circles= O and O'
Radii = 10 and 8cm
common chord= PQ
OP= 10cm
O'P = 8cm
PQ= 12cm
PL= 1/2PQ
= 1/2 x 12
= 6cm

In right angle triangle OLP

OP² = OL² + LP²
OL= √OP² - LP²
= √10²- 6²
= √64
= 8cm

In right angle triangle O'LP

O'P²= O'L² - LP²
O'L= √O'P² - LP²
= √8² - 6²
= √28
= 5.29 cm

OO'= 8 + 5.29
= 13.29 cm

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