Given a rectangle ABCD, the diagonals AC and BD intersect at point O. Find OC if BD = 11.

univerkov | September 4, 2021 | education

Since ABCD is a rectangle, AB = CD, BC = AD and AB || Sun, sun || AD.

Then right-angled triangles ABD and ACD are equal in two legs, then AC = BD = 11 cm.

Triangles BOC and AOD are equal in side and two adjacent angles, BC = AD, angle OBC = ODA, angle OCB = OAD as criss-crossing angles.

Then OS = OA, OB = OD, and then point O is the middle of the diagonals AC and BD, which means OC = AC / 2 = 11/2 = 5.5 cm.

Answer: The length of the OC segment is 5.5 cm.

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