What is the radius of the circumscribed circle of a right triangle?

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The hypotenuse of the triangle is the diameter of its circumcircle, and the circumcenter is its midpoint, so the circumradius is equal to half of the hypotenuse of the right triangle.

What does it mean when a triangle is circumscribed about 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 is the formula of radius of circumcircle?

Circumcircle of a triangle, radius = 4×s(s−a)(s−b)(s−c) abc.

How can you circumscribe a circle about a triangle big ideas?

Use a compass and straightedge to construct a circle that is circumscribed about △ABC. Draw a bisector Draw the perpendicular bisector of — AB . Draw a bisector Draw the perpendicular bisector of — BC . Label the intersection of the bisectors D.

How do u find the radius of a triangle?

For any triangle △ABC, let s = 12 (a+b+c). Then the radius r of its inscribed circle is r=Ks=√s(s−a)(s−b)(s−c)s.

What is the equation of the circle inscribed in 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.

How do you circumscribe a circle about a triangle?

– Construct the perpendicular bisector of one side of triangle. – Construct the perpendicular bisector of another side. – Where they cross is the center of the Circumscribed circle. – Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your Circumscribed circle!

How to find the circumcircle of a triangle?

Find 2 lines (say PQ and QR) which form the sides of the triangle.

Find the perpendicular bisectors of PQ and QR (say lines L and M respectively).

Find the point of intersection of lines L and M as the circumcenter of the given triangle.

How to construct the circumcenter of a triangle?

Draw the perpendicular bisector of any two sides of the given triangle.

Using a ruler,extend the perpendicular bisectors until they intersect each other.

Mark the intersecting point as P which will be the circumcenter of the triangle.

What is the center of a circle inscribed in a triangle?

A circle is inscribed in the triangle if the triangle’s three sides are all tangents to a circle. In this situation, the circle is called an inscribed circle, and its center is called the inner center, or incenter.