You have enough lengths now, and some right angle triangles, so you can compute OE and EQ! Note that E splits the chord AB so you know AE, EB. If you drop the circles you can then focus on the two isosceles triangles One good way to do this type of problem is to shift your attention.ĭraw in the radii: OA, OB, QA,QB all of which you know. Since triangles AQC and ACO are right triangles you can use Pythagoras' theorem to find the lengths of QC and CO. By the symmetry C is the midpoint of AB and the angles ACO and QCA are right angles. Thanks.Ĭ is the intersection of the line segments AB and OQ. I would appreciate any help on this problem. If AB is 6 and circle O has a radius of length 4 (horizontal line going through the overlapping circles and touching the side of the circle) and circle Q has a radius of length 6, how long is OQ. Two overlapping circles O and Q have the common chord AB (vertical line between the overlapping circles). G.I've looked all over and cannot find out how to solve this problem. a common internal tangent to circles O and P
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