Geometry Unit Circles

A circle has a radius of 20 centimeters and a central angle that measures 216 degrees. Find the length of the arc defined by this central angle.

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HSG-C.B

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HSG-C.B.5

Tyler bought a wedge. He measured the arc length of the wedge to be 12 centimeters and the radius to be 8 centimeters. Priya bought a wedge that came from a circular cheese block with radius 9 centimeters. The block was cut into 6 congruent sectors. Whose wedge is larger? Explain or show your reasoning.

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HSG-C.B.5

The radius of a circle measures 12 centimeters. What is the circumference of the circle?

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7.G.B.4

The radius of a circle measures 12 centimeters. What is the area of the circle?

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7.G.B.4

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HSG-C.B

Find the area of the shaded region of the circle. The radius is given in inches.

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HSG-C.B

Triangle (ABC) is shown with its incenter at (D). The inscribed circle’s radius measures 2 units. The length of (AB) is 9 units. The length of (BC) is 10 units. The length of (AC) is 17 units. What is the area of triangle (ACD)?

• 17 square units

• 36 square units

Triangle \(ABC\) is shown with its incenter at \(D\). The inscribed circle’s radius measures 2 units. The length of \(AB\) is 9 units. The length of \(BC\) is 10 units. The length of \(AC\) is 17 units. What is the area of triangle \(ABC\)?

• 17 square units

• 36 square units

Triangle \(ABC\) is shown with an inscribed circle of radius 4 units centered at point \(D\). The inscribed circle is tangent to side \(AB\) at the point \(G\). The length of \(AG\) is 6 units and the length of \(BG\) is 8 units. What is the measure of angle \(A\)?

• \(\arctan\left(\frac{2}{3}\right)\)

• \(2\arctan\left(\frac{2}{3}\right)\)

• \(\arcsin\left(\frac{2}{3}\right)\)

• \(2 \arccos\left(\frac{2}{3}\right)\)