# Math Help - Circumference

1. ## Circumference

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?

2. Originally Posted by 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?
Have you drawn the picture?

3. Originally Posted by dwsmith
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 ?

4. Originally Posted by 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?
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?

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

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

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

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

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