Through a point on the surface of the ball, two sections of the ball are drawn by planes equidistant

| April 28, 2021 | education

Through a point on the surface of the ball, two sections of the ball are drawn by planes equidistant from the center of the ball. The angle formed by the section planes is 120. The distance from the center of the ball to the section plane is 2 root of 3. Find the radius of the ball.

Let us draw from the center of the circle of the point O the radius OA, where A is the common point of the sections of the ball. Since the sections are equidistant from the center of the ball, then ОВ = OC 2 * √3 cm.

In right-angled triangles AOB and AOC, the hypotenuse of OA is common, and the legs of OB and OS are equal, then the triangles are equal in leg and hypotenuse.

Then the angle BAO = CAO, and their sum is 120, then the angle BAO = CAO = 120/2 = 60.

In a right-angled triangle AOB, Sin60 = BO / OA.

OA = R = BO / Sin60 = 2 * √3 / (√3 / 2) = 4 cm.

Answer: The radius of the ball is 4 cm.



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