A circle is inscribed in an angle of 60 °. Find the distance from the center of the circle to the apex

| June 15, 2021 | education

A circle is inscribed in an angle of 60 °. Find the distance from the center of the circle to the apex of the corner if the radius of the circle is 7.5.

From point O, the center of the circle, we draw the radii OA and OB to the points of tangency A and B.

By the property of tangents, the radius drawn to the point of tangency is perpendicular to the tangent itself, then the angle ОАС = ОВС = 90.

Let us prove that right-angled triangles AOB and AOC are equal.

The hypotenuse of the OC in triangles is common, the leg OA = OB as the radii of the circle, then the triangles are equal in the leg and the hypotenuse, and therefore the angle ACO = BCO = ACB / 2 = 60/2 = 30.

The leg of the OB of a right-angled triangle of the COB is located opposite an angle of 30, then OС = 2 * OB = 2 * 7.5 = 15 cm.

Answer: From the center of the circle to the top of the corner 15 cm.



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