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
$cp = \sqrt{64 + 36} = \sqrt{100} = 10$
according to Pythagorean theorem:

CM=
$cm = \sqrt{10^{2} - 4 ^{2} } = \sqrt{100 - 16} = \sqrt{84} = 2 \sqrt{21}$
AC=2CM=
$2 \times 2 \sqrt{21} = 4 \sqrt{21}$

PB=CP=10
according to Pythagorean theorem:

BN=
$bn = \sqrt{10^{2} - {2}^{2} } = \sqrt{100 - 4} = \sqrt{96} = 4 \sqrt{6}$


AB=2BN
$ab = 2 \times 4 \sqrt{6} = 8 \sqrt{6}$