The intersection point of the diagonals is in the rectangle ABCD O. BH and DE are the heights of the ABO

| March 17, 2021 | education

The intersection point of the diagonals is in the rectangle AВСD O. BH and DE are the heights of the ABO and СOD triangles, respectively, the angle BOH = 60 degrees, AH = 5 cm. Find OE.

Consider a triangle AOB, in which OA = OB, as halves of the diagonals AC and BD, which are halved at point O. Since in an isosceles triangle one of the angles is 60, the AOB triangle is equilateral. The height of the ВН in the equilateral triangle ABO is also the median, then AH = OH = AO / 2 = 5/2 = 2.5 cm.

Triangles BOH and DOE are rectangular, and the angle BOH = DOE = 60 as vertical angles, OB = OD as half of the diagonals, then triangle BON is equal to triangle DOE in hypotenuse and acute angle, which means OE = OH = 2.5 cm.

Answer: The length of the segment OE is 2.5 cm.



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