How do you find the Centre of a circumscribing circle of a triangle?
Circumscribed circles When a circle circumscribes a triangle, the triangle is inside the circle and the triangle touches the circle with each vertex. find the midpoint of each side. Find the perpendicular bisector through each midpoint. The point where the perpendicular bisectors intersect is the center of the circle.
What is the equation of the circle circumscribing the triangle with vertices?
The square of the distance from that midpoint to any of the three vertices is the square of the radius of the circle, thus (3/2)² + (3/2)² = 9/2.
How do you find the equation of a circle of a circle?
Correct answer: The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
How do you find the radius of a circle in a circumscribing triangle?
For a triangle △ABC, let s = 12 (a+b+ c). Then the radius R of its circumscribed circle is R=abc4√s(s−a)(s−b)(s−c). In addition to a circumscribed circle, every triangle has an inscribed circle, i.e. a circle to which the sides of the triangle are tangent, as in Figure 12.
How do you find the equation of a circle with vertices?
We know that the general equation for a circle is ( x – h )^2 + ( y – k )^2 = r^2, where ( h, k ) is the center and r is the radius.
What is the equation of a circle definition?
A circle is the set of all points in a plane at a given distance (called the radius ) from a given point (called the center.) The equation of a circle with center (h,k) and radius r units is (x−h)2+(y−k)2=r2 .
What is the radius of a circle circumscribing an equilateral triangle?
The radius of a circumcircle of an equilateral triangle is equal to (a / √3), where ‘a’ is the length of the side of equilateral triangle.
How do you find the radius of a circle equation?
The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being “r”. This form of the equation is helpful, since you can easily find the center and the radius.