Geometry
# Inscribed and Circumscribed Figures

In the above diagram, circle \(O\) is the incircle of right triangle \(ABC.\) Given the two side lengths \[\lvert\overline{AB}\rvert = 7 \text{ and }\lvert\overline{BC}\rvert = 16,\] what is the area of the circle?

**Note:** The above diagram is not drawn to scale.

In the above diagram, circle \(O\) is inscribed in triangle \(\triangle ABC,\) with points of contact \(D, E,\) and \(F\). If \(\angle DBE = 54^{\circ} \text{ and } \angle DAF = 46^{\circ},\) what is \(\angle BOC?\)

**Note:** The above diagram is not drawn to scale.

In the above diagram, circle \(O\) is inscribed in \(\triangle ABC\), with points of contact at points \(D, E\) and \(F\). If \(a=4, b=7\) and \(c=9,\) what is the perimeter of triangle \(\triangle ABC?\)

**Note:** The above diagram is not drawn to scale.

×

Problem Loading...

Note Loading...

Set Loading...