In the figure shown, square wxyz is inscribed in circle O. Also, OM ⊥ XY and OM=7. Find the area of…

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Tanong

In the figure shown, square wxyz is inscribed in circle O. Also, OM ⊥ XY and OM=7. Find the area of the shaded region.

Mga sagot sa #1 sa Tanong: In the figure shown, square wxyz is inscribed in circle O. Also, OM ⊥ XY and OM=7. Find the area of the shaded region.

Answer: C. 98π-196

Step-by-step explanation:

calculate the area of the square inside:

since from the mid point to the sides is 7, then the whole length will be 14.

14 × 14 =196

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use Pythagorean theorem to find the radius of the circle:

utilizing the square, the radius will be the length from mid-point to the edge or angle of the square.

since OM is half of the whole length and M is the midpoint of XY (because O is the midpoint of the square or circle and OM is perpendicular to XY) we can get that OM=XY

as OM=XY, they form a right triangle, we can use a²+b²=c² to find the hypotenuse

7²+7²=(7√2)²

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find the area of the circle:

formula is πr²

the radius is 7√2

(7√2)²π=98π

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find the shaded region:

in order to find the shaded region, we need to subtract the square from the circle.

98π-196


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