# In rectangle ABCD, point O is the point of intersection of the diagonals, BH

July 26, 2021 | education

| **In rectangle ABCD, point O is the point of intersection of the diagonals, BH and DE of the heights of triangles ABO and COD, respectively, with the angle BOH = 60 degrees, AH = 5 centimeters. Find OE.**

In the triangle AOB OA = OB, as half the diagonals of the rectangle, therefore, triangle AOB is isosceles, and since the angle AOB, according to the condition, is 60, then AOB is equilateral. The height of BH in an equilateral triangle AOB is the height, median and bisector, then OH = AH = 5 cm.

Triangles AOB and COD are equal on three sides, then the triangle SOD is equilateral, and therefore DE is the median of the triangle, and OE = OH = 5 cm.

Answer: The length of the segment OE is 5 cm.

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