The radius of the circle is 10 cm, and the distance from one end of the diameter to the point of the circle is 16 cm. Find the distance from the other end of the diameter to this point.
Let AC – diameter, AO – radius, AB – distance from a point to one end of the diameter, BC – distance from a point to the other end of the diameter.
AC = 2 * AO = 2 * 10 = 20 (cm).
In triangle ABC, draw the median BO (BO is also the radius of the circle). Then triangle AOB is isosceles with base AB = 16 cm.
Consider the BOC triangle. BОС – isosceles triangle with lateral sides BО = ОС = 10 cm.Then triangle BОС = triangle AOB, therefore BC = AB = 16 cm.
Answer: BC = 16 cm.
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