×
Geometry

# Tangent - Subtended Arc

Circle $$O$$ with radius $$2$$ is inscribed in a trapezoid $$ABCD$$ such that $$\overline{AD} \parallel \overline{BC}$$ and $$\lvert \overline{CD} \rvert = 8.$$ If $$\angle{A} = \angle{B} = 90^{\circ},$$ what is the area of $$ABCD?$$

Note: The above diagram is not drawn to scale.

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

Note: The above diagram is not drawn to scale.

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

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

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

×