
Neal D. answered 09/03/16
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Draw the two intersecting circles and label as follows:
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
Radius drawn perpendicular to a chord will bisect the chord
You now have four right triangles formed by the radii of each
circle with the perpendicular drawn from each center point
to the chord of intersection, we will use one triangle from
each circle
OB = 8, BI = 6, find OI by Pythagorean Theorem
BI2 + OI2 = OB2
36 + OI2 = 64
OI2 = √ 28
OI = 5.292
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BP = 10, BI = 6, find PI
This is a 3 - 4- 5 right triangle: 6, PI = 8, 10
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Therefor the distance between the centers:
PO = OI + BI
PO = 5.292 + 8
PO = 13.292 ; Your answer would be : 4