The centers of two intersecting circles are located on opposite sides of their common chord.

| April 2, 2021 | education

The centers of two intersecting circles are located on opposite sides of their common chord. The chord is equal to a and serves in one circle as the side of a regular inscribed triangle, and in the other – as an inscribed square. Find the distance between the centers of these circles.

The distance between the centers of the circle OO1 = O1H + OH.

Since a square is inscribed in one of the circles, the distance OH is equal to half the length of the side of the square. OH = BC / 2 = a / 2.

A regular triangle with a side equal to a cm is inscribed in another circle.

The О1Н distance is equal to the radius of the inscribed circle in the ABC triangle.

О1Н = a * √3 / 6.

Then OO1 = a * √3 / 6 + a / 2 = a * √3 / 6 + 3 * a / 6 = (a / 6) * (3 + √3) see.

Answer: The distance between the centers of the circle is (a / 6) * (3 + √3) cm.



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