NL and CK are the diameters of a circle with center O. what will be the perimeter of the triangle NOK

univerkov | March 1, 2021 | education

NL and CK are the diameters of a circle with center O. what will be the perimeter of the triangle NOK if it is known that CL = 23 cm, NL = 28 cm.

Consider triangles COL and NKO and prove that these triangles are equal.

Lines ON = OK = OL = OC = NL / 2 = 28/2 = 14 cm as circle radii.

Angle NOK = COL as vertical angles. Then the triangles COL and NKO are equal in two sides and the angle between them.

Since in equal triangles the corresponding sides are equal, then NK = CL = 23 cm.

Determine the perimeter of the triangle NOK.

Pnok = NO + KO + NK = 14 + 14 + 23 = 51 cm.

Answer: The perimeter of the triangle NOK is 51 cm.

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