Geometry

Tangent and Secant Lines

Tangent - Subtended Arc

         

Circle OO with radius 22 is inscribed in a trapezoid ABCDABCD such that ADBC\overline{AD} \parallel \overline{BC} and CD=8.\lvert \overline{CD} \rvert = 8. If A=B=90,\angle{A} = \angle{B} = 90^{\circ}, what is the area of ABCD?ABCD?

Note: The above diagram is not drawn to scale.

In the above diagram, BC,AE\overline{BC}, \overline{AE} and AF\overline{AF} are tangent to circle OO at D,ED, E and F,F, respectively. If AC=25,AB=20,BC=15,\lvert \overline{AC} \rvert = 25, \lvert \overline{AB} \rvert = 20, \lvert \overline{BC} \rvert = 15, what is the area of quadrilateral CDOF?CDOF?

Note: The above diagram is not drawn to scale.

In the above diagram, AB\overline{AB} and CB\overline{CB} are both tangent to circle DD and are perpendicular to each other. If the length of AB\overline{AB} is 8,8, what is the area of the quadrilateral ABCD?ABCD?

In the above diagram, AP\overline{AP} and AQ\overline{AQ} are tangent to circle OO at PP and Q,Q, respectively. If the length of AP\overline{AP} is AP=13\lvert \overline{AP} \rvert = 13 and PAQ=60\angle{PAQ} = 60^{\circ}, what is the area of the shaded region?

Given the quadrilateral and inscribed circle, what is the missing side length?

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