2 circles whose radii of 20 and 21 cm pass through the point M tangents to them at this point

2 circles whose radii of 20 and 21 cm pass through the point M tangents to them at this point are mutually perpendicular find the distance between the centers of the circle

By condition, the tangent at the point M is perpendicular. Let’s draw the radii ОМ and О1М to the tangent M. Since the radius of the circle drawn to the tangent is perpendicular to the tangent, the triangle OO1M is rectangular at the vertex M.

By the Pythagorean theorem, we define the hypotenuse OO1, which is the distance between the centers of the circles.

OO1 ^ 2 = OM ^ 2 + O1M ^ 2 = 20 ^ 2 + 21 ^ 2 = 400 + 441 = 841.

OO1 = 29 cm.

Answer: The distance between the centers of the circle is 29 cm.