How do you find the equation of a circle circumscribing a triangle?

The equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5 is. Let P(a, b) be the centre of the circle. On simplification, we get the equation, x² + y² – 17x – 19y + 50 = 0, which is the required equation.

How do you find the equation of a circle that circumscribes a triangle?

Given A, B, and C as the sides of the triangle and A as the area, the formula for the radius of a circle circumscribing a triangle is r = ABC / 4A and for a circle inscribed in a triangle is r = A / S where S = (A + B + C) / 2.

What is the area of triangle that circumscribing a circle?

Theorem 2 can be used to derive another formula for the area of a triangle: Theorem 3. For a triangle △ABC, let K be its area and let R be the radius of its circumscribed circle. Then K=abc4R(and hence R=abc4K).

What is the meaning of triangle circumscribing a circle?

A triangle is called a circumscribed triangle when a circle passes through all three vertices of the triangle. The circumscribed circle's centre is the triangle's circumcenter; this is the point where the perpendicular bisectors of the sides meet.

What does mean by circumscribing?

circumscribe \SER-kum-skrybe\ verb. 1 a : to constrict the range or activity of definitely and clearly. b : to define or mark off carefully. 2 a : to draw a line around. b : to surround by or as if by a boundary.

Find the equation of circle circumscribing the triangle formed by the lines 2x+y=4, x+y=6 and x+2y=5

What is the area of an equilateral triangle circumscribing a circle of radius 6 cm?

Summary: If a circle has a radius of 6 cm then the area of an inscribed equilateral triangle is 27√3 cm².

What is the area of an equilateral triangle whose inscribed circle has radius?

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa²/12. Lets see how this formula is derived, Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.

What is the length of an equilateral triangle inscribed in a circle?

Length BD=length DC. Total length BC= BD+DC. BC=2×3√3=6√3cm. Note: If the question was given for isosceles triangle instead of equilateral triangle, the OA≠OB≠OC ≠radius.

How do you find the circumference of a circle with a triangle inside?

Find The Circumference Of A Circle : Example Question #6

Explanation: If a right triangle is inscribed inside a circle, then the arc intercepted by the right angle is a semicircle, making the hypotenuse of triangle a diameter. This is the diameter, also, so the circumference is \displaystyle C = \pi d = 30 \pi.

What is the meaning of circumscribing a square?

If you circumscribe a triangle, square, etc., you draw a circle that surrounds it and touches each of its corners.

Can any triangle be circumscribed?

Every triangle can be circumscribed by a circle, meaning that one circle — and only one — goes through all three vertices (corners) of any triangle. In laymen's terms, any triangle can fit into some circle with all its corners touching the circle.

What is a circumscribed angle?

A circumscribed angle is the angle made by two intersecting tangent lines to a circle.

What is the relation between circle and equilateral triangle?

Properties of a Circumcircle are as follows:

Circumscribed circle of an equilateral triangle is made through the three vertices of 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 height of an equilateral triangle inscribed in a circle?