Diameters AB and CD are drawn in a circle with center O. What is the perimeter of triangle AOD

univerkov | August 16, 2021 | education

Diameters AB and CD are drawn in a circle with center O. What is the perimeter of triangle AOD, if AB = 12 cm, BC = 5 cm?

Since the diameter of the circle is divided in half at the center, then:

AO = 1/2 * AB = 1/2 * 12 = 6 cm.

Triangles AOD and COB are equal on two sides and the angle between them (the angles AOD and COB are vertical), then:

AD = BC = 5 cm.

The perimeter of the AOD is:

P = AD + 2 * AO = 5 + 2 * 6 = 17 cm.

Answer: the desired perimeter is 17 cm.

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