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 ?
Answer & explanation
Correct answer: option 1
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