A circle is inscribed in the rhombus. The point of tangency divides the side of the rhombus into segments, 1 cm and 14 cm. What is the diameter of the circle?
From the point O, the center of the circle, we construct a perpendicular to the point H, the point of tangency.
The radius drawn to the tangent point is perpendicular to the tangent itself.
The AOB triangle is rectangular, since the diagonals of the rhombus intersect at right angles.
Then OH is the height drawn to the hypotenuse from the top of the right angle.
OH ^ 2 = AH * BH = 14 * 1 = 14.
OH = √14 cm.
Then НК = D = 2 * √14 cm.
Answer: 3) the diameter of the circle is 2 * √14 cm.
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