The radius of the circumscribed circle of triangle ABC is radius of the circumscribed circle is approximately 1.3. Option A is the right choice.
The radius of the circumscribed circle of a triangle is the distance from the circumcenter of the triangle to any of its vertices. The circumcenter is the point where the perpendicular bisectors of the sides of the triangle intersect.
To find the radius of the circumscribed circle of triangle ABC, we can use the following formula:
R = abc / 4√s(s - a)(s - b)(s - c)
where:
R is the radius of the circumscribed circle
a, b, and c are the side lengths of the triangle
s is the semiperimeter of the triangle, which is equal to (a + b + c) / 2
From the image, we can measure the side lengths of triangle ABC as follows:
AB = 5 units
BC = 9 units
CA = 12 units
Using the formula above, we can calculate the semiperimeter of the triangle:
s = (AB + BC + CA) / 2 = (5 units + 9 units + 12 units) / 2 = 13 units
Now we can calculate the area of the triangle using Heron's formula:
K = √s(s - a)(s - b)(s - c)
where K is the area of the triangle.
Plugging in the values we calculated for s, a, b, and c, we get:
K = √13(13 - 5)(13 - 9)(13 - 12) = 24√5
Finally, we can calculate the radius of the circumscribed circle:
R = abc / 4√s(s - a)(s - b)(s - c) = (5 * 9 * 12) / (4 * 24√5) = 1.3 units
Therefore, the radius of the circumscribed circle of triangle ABC is 1.3 units.
So the answer is A. 1.3.
Question:-
What is the radius of the circumscribed circle of △ABC?
A. 1.3
B. 5.8
C. 4.0
D. 5.6