OK is the bisector of the angle AOB shown in the figure. Find AK if KB = 12 and ОА = ОВ.

Since OB is the bisector of the angle AOB, then the angle AOK = VOK.

Consider triangles AOK and BOK, which have a common side OK, side OA = OB from the condition, angle AOK = BOK, since OK is a bisector.

Then the triangles AOB and BOK are equal on two sides and the angle between them – the first sign of equality of triangles.

Then AK = BK = 12 cm.

Answer: The length of the AK segment is 12 cm.

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