# Circumference

#### winsome

Triangle ABC is circumscribed about cirlce O. P and Q are points of tangency such that BP=3 and CQ=5. Waht is the measure of BC?

#### dwsmith

MHF Hall of Honor
Triangle ABC is circumscribed about cirlce O. P and Q are points of tangency such that BP=3 and CQ=5. Waht is the measure of BC?
Have you drawn the picture?

#### winsome

Have you drawn the picture?
Yeah, I have drawn a picture but i want to know that how i can find the measure of BC ?

#### dwsmith

MHF Hall of Honor
Triangle ABC is circumscribed about cirlce O. P and Q are points of tangency such that BP=3 and CQ=5. Waht is the measure of BC?
P and Q are tangent points. These points can't be on the circle then because if triangle ABC is inscribed inside and the points are on the circle, then they are secant points. Where did you put these points on the drawing?

#### Soroban

MHF Hall of Honor
Hello, winsome!

Triangle ABC is circumscribed about cirlce O.
P and Q are points of tangency such that BP = 3 and CQ = 5.
What is the measure of BC?
Code:
                        A
o
/ \
/   \
/     \
/       \
/         \
/   * * *   \
/*           *\
*               *
P o                 o Q
/                   \
/*                   *\
/ *         *         * \
3 /  *         O         *  \ 5
/                           \
/     *                 *     \
/       *               *       \
/          *            *         \
B o - - - - - - - * o * - - - - - - - o C
3         R         5

Side $$\displaystyle AB$$ is tangent to the circle at $$\displaystyle P.$$
Side $$\displaystyle AC$$ is tangent to the circle at $$\displaystyle Q.$$
Side $$\displaystyle BC$$ is tangent to the circle at $$\displaystyle R.$$

We are given: .$$\displaystyle BP \,=\,3,\;CQ \,=\,5.$$

The tangents drawn from an external point to a circle are equal.

. . Hence: .$$\displaystyle BR = 3,\;CR = 5.$$

Therefore: .$$\displaystyle BC \;=\;3 + 5 \;=\;8$$

bjhopper