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Three tangent circles of radius 10 cm are drawn. All centers lie on the line AB. The tangent AC to the right-hand circle is drawn, intersecting the middle circle at D and E. Find the length of the segment DE.

 Nov 15, 2021
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Three tangent circles of radius 10 cm are drawn. All centers lie on line AB. The tangent AC to the right-hand circle is drawn, intersecting the middle circle at D and E. Find the length of the segment DE.

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AC = sqrt(AB2 - BC2)

Mid point of AC => F

Center of middle circle => G

AG = 2r

FG / AG = BC / AB         FG = (AG * BC) / AB

DE = 2 * sqrt(DG2 - FG2)

 Nov 17, 2021

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