The drawing shows an isosceles triangle PQR. Each vertex of triangle PQR is a point on circle O. If the circumference of circle O is 10π units, what is the area of triangle PQR? Areatriangle=21bhA 100 sq units B 50 sq units C 30 sq units D PQR0 sq units
Q. The drawing shows an isosceles triangle PQR. Each vertex of triangle PQR is a point on circle O. If the circumference of circle O is 10π units, what is the area of triangle PQR? Areatriangle=21bhA 100 sq units B 50 sq units C 30 sq units D PQR0 sq units
Calculate Circle Radius: Calculate the radius of circle O using the circumference formula C=2πr.Circumference = 10π=2πrr = 2π10π=5 units
Identify Triangle Type: Identify the type of triangle PQR. Since PQR is isosceles and each vertex lies on the circle, it forms an isosceles triangle with two equal sides.
Calculate Base and Height: Calculate the base and height of triangle PQR. Since it's inscribed in a circle, the base can be considered as the diameter of the circle.Base (b)=2r=2×5=10 units
Calculate Triangle Height: Calculate the height h of the triangle using the Pythagorean theorem in one of the right triangles formed by the altitude.Let's assume the height divides the base into two equal parts of 5 units each.Using Pythagoras theorem, h2+52=52h2=52−52=0h=0