The diameter MP, chords MK and PK are drawn in the circle. Find the area of the triangle MPK if MK = 14, PK = 6.

Since, by condition, МР is the diameter of a circle, then the degree measure of the arc MKР is equal to half of the degree measure of the circle. Arc MKR = 360/2 = 180. Arc MP = (360 – 180) = 180.

The inscribed angle MKP rests on the arc MP and is equal to half of its degree measure.

Angle MKР = 180/2 = 900.

Then the triangle MKР is rectangular, and the chords MK and PK are its legs.

The area of the MKР triangle is equal to: Smcr = MK * РK / 2 = 14 * 6/2 = 42 cm2.

Answer: The area of the MKР triangle is 42 cm2.