the area of a circle?

Question

a triangle is inscribed in a a circle and the triangle has sides 5,12, and 13. find the part of the area of the of the circle that doesn't overlap with the area of the triangle.

Answer 1

It's a right triange because 5^2 + 12^2 = 13^2. So, the radius of the circle must be 13.

area of circle = 169 * pi

area of triangle = 5 * 12 / 2 = 30

The non-overlapping part of the circle is the difference of the two

Answer 2

The circle has diameter of 13 because this is a right triangle (why? try 5² + 12² = x² and find x) with hypotenuse equal 13, and the hypotenuse of a right triangle is always the longest side and always opposite the right angle. Since a right angle inscribed in any circle always subtends an arc measure equal to half the angular measure of the circle (360°/2 = 180°), the endpoints of the chord which intersect the ends of the subtended arc are the endpoints of the diameter. Hence, the side opposite the right angle in any right triangle inscribed in a circle is the diameter.

Since in this particular circle the diameter is 13, then the radius is 6.5, or half of that.

Area of circle = pi r² = pi (13/2)² = pi (6.5)² = 42.25 pi sq units

Area of triangle = ½ b h = (½)(5)(12) = 30 sq units

The area of the circle you are interested in is this:

Area of circle - Area of triangle = (42.25 pi - 30) sq units

Answer 3

I assume you mean the length of the triangle's sides are 5, 12 and 13 units. We must choose a value for pi so I choose 3.14159

The total area of the circle is approximately 132.73
The area of the triangle is 30 (half that of a 5 x 12 rectangle made from 2 of the triangles)
The area of the circle outside the triangle is approximately 102.72

Answer 4

5*5+12*12=25+144=169=13*13
So, the triangle is right-angled triangle.
Therefore, the radius of the circle is 13/2=6.5 and the area is pi*r^2=pi*42.25
the area of the rectangle is 5*12/2=30
And the required area is pi*42.25-30 ~= 102.73

Answer 5

trie pie times radious squared plus the triangles area