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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?

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 questio class=

Respuesta :

Awste
radius is CP

according to Pythagorean theorem:
CP^2=8^2+6^2
[tex]cp = \sqrt{64 + 36} = \sqrt{100} = 10[/tex]
according to Pythagorean theorem:

CM=
[tex]cm = \sqrt{10^{2} - 4 ^{2} } = \sqrt{100 - 16} = \sqrt{84} = 2 \sqrt{21} [/tex]
AC=2CM=
[tex]2 \times 2 \sqrt{21} = 4 \sqrt{21} [/tex]

PB=CP=10
according to Pythagorean theorem:

BN=
[tex]bn = \sqrt{10^{2} - {2}^{2} } = \sqrt{100 - 4} = \sqrt{96} = 4 \sqrt{6} [/tex]


AB=2BN
[tex]ab = 2 \times 4 \sqrt{6} = 8 \sqrt{6} [/tex]


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