Triangle PQR is inscribed in the circle whose radius is 13 cm. IF PQ is the diameter of the circle and PR = 10 cm, then what is the area of the triangle PQR ?

120

Diameter PQ = 13 × 2 = 26 cm

∠PRQ = 90°  (angle in semicircle)

∴  using pythagorus theorem

PQ² = PR² + RQ²

RQ = \(\sqrt {PQ^2 - PR^2}\)

RQ = \(\sqrt {(26)^2 - (10)^2}\)

     =  \(\sqrt {36 × 16}\)  =  6 × 4

RQ = 24 cm

Area of PQR = \(\frac{1}{2}\) × 24 × 10  =  120 cm²