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A right triangle △ABC with right angle C is inscribed in a circle. Find the radius of this circle if: Given m∠C = 90°, k(O, r) inscribed in △ABC, AC = 8 cm, BC = 6 cm. Find r.

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4 votes

Answer:

The radius is
r=5\ cm

Explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so


m<C =(1/2)[arc\ AB]


m<C =90\°

substitute


90\°=(1/2)[arc\ AB]


arc\ AB=180\°

That means----> The length side AB of the inscribed triangle is a diameter of the circle

Applying Pythagoras Theorem

Calculate the length side AB


AB^(2)=AC^(2)+BC^(2)


AB^(2)=8^(2)+6^(2)


AB^(2)=100


AB=10\ cm -----> is the diameter

Find the radius


r=10/2=5\ cm -----> the radius is half the diameter

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