Question

In the diagram below, ΔABC is inscribed in circle P. The distances from the center of circle P to each side of the triangle are shown.

Answer the following questions:
What is the length of the radius of the circle shown?
What is the length of AB and AC?

Answer 1

radius is CP

according to Pythagorean theorem:
CP^2=8^2+6^2

`cp = √(64 + 36) = √(100) = 10`
according to Pythagorean theorem:

CM=

`cm = \sqrt{10^(2) - 4 ^(2) } = √(100 - 16) = √(84) = 2 √(21)`
AC=2CM=

`2 * 2 √(21) = 4 √(21)`

PB=CP=10
according to Pythagorean theorem:

BN=

`bn = \sqrt{10^(2) - {2}^(2) } = √(100 - 4) = √(96) = 4 √(6)`


AB=2BN

`ab = 2 * 4 √(6) = 8 √(6)`