Waste less time on Facebook — follow Brilliant.
×
Geometry

Tangent and Secant Lines

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?

×

Problem Loading...

Note Loading...

Set Loading...