Two circles of radii 10cm and 8cm intersect at the point p and q. if pq = 12cm. and the distance between the centres of the circle is x cm . the value of x
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Answer:
13.29 cm
Step-by-step explanation:
Two circles of a radii 10cm and 8cm intersect and the length of the common chord is 12cm. find the distance between the centers
Answer
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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