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The drawing shows an isosceles triangle PQRPQR. Each vertex of triangle PQRPQR is a point on circle OO. If the circumference of circle OO is 10π10\pi units, what is the area of triangle PQRPQR? Areatriangle=12bh\text{Area}_{\text{triangle}} = \frac{1}{2} bh \newlineA 100100 sq units \newlineB 5050 sq units \newlineC 3030 sq units \newlineD PQRPQR00 sq units

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Q. The drawing shows an isosceles triangle PQRPQR. Each vertex of triangle PQRPQR is a point on circle OO. If the circumference of circle OO is 10π10\pi units, what is the area of triangle PQRPQR? Areatriangle=12bh\text{Area}_{\text{triangle}} = \frac{1}{2} bh \newlineA 100100 sq units \newlineB 5050 sq units \newlineC 3030 sq units \newlineD PQRPQR00 sq units
  1. Calculate Circle Radius: Calculate the radius of circle OO using the circumference formula C=2πrC = 2\pi r.\newlineCircumference = 10π=2πr10\pi = 2\pi r\newliner = 10π2π=5\frac{10\pi}{2\pi} = 5 units
  2. Identify Triangle Type: Identify the type of triangle PQRPQR. Since PQRPQR is isosceles and each vertex lies on the circle, it forms an isosceles triangle with two equal sides.
  3. Calculate Base and Height: Calculate the base and height of triangle PQRPQR. Since it's inscribed in a circle, the base can be considered as the diameter of the circle.\newlineBase (b)=2r=2×5=10(b) = 2r = 2 \times 5 = 10 units
  4. Calculate Triangle Height: Calculate the height hh of the triangle using the Pythagorean theorem in one of the right triangles formed by the altitude.\newlineLet's assume the height divides the base into two equal parts of 55 units each.\newlineUsing Pythagoras theorem, h2+52=52h^2 + 5^2 = 5^2\newlineh2=5252=0h^2 = 5^2 - 5^2 = 0\newlineh=0h = 0

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