If two circles of radii 10cm and 8cm intersect each other and the length of the common chord is 12cm find the distance between their centers
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Circle O with radius 8; circle P with radius 10 AB is chord of intersection and has length = 12 I is point on the chord where the radii of the two cirlcles will meet
∴OB = 8, BI = 6, find OI by Pythagorean Theorem
BI2 + OI2 = OB2 36 + OI2 = 64 OI2 = √ 28 OI = 5.292-------------------------------------------------------------- BP = 10, BI = 6, find PI This is a 3 - 4- 5 right triangle: 6, PI = 8, 10-------------------------------------------------------------- Therefor the distance between the centers: PO = OI + BI PO = 5.292 + 8 PO = 13.292
∴4 IS THE ANSWER
∴OB = 8, BI = 6, find OI by Pythagorean Theorem
BI2 + OI2 = OB2 36 + OI2 = 64 OI2 = √ 28 OI = 5.292-------------------------------------------------------------- BP = 10, BI = 6, find PI This is a 3 - 4- 5 right triangle: 6, PI = 8, 10-------------------------------------------------------------- Therefor the distance between the centers: PO = OI + BI PO = 5.292 + 8 PO = 13.292
∴4 IS THE ANSWER
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