# What size triangle fits in a circle?

## What size triangle fits in a circle?

An equilateral triangle in a circle. Question: An equilateral triangle is drawn within a circle such that all three points of the triangle just touch the inside of the circle.

## How do you find the radius of a triangle inscribed in a circle?

For any triangle △ABC, let s = 12 (a+b+c). Then the radius r of its inscribed circle is r=(s−a)tan12A=(s−b)tan12B=(s−c)tan12C.

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

To find the area of an equilateral triangle inscribed in a circle, we have to find the length of the side of the equilateral triangle. Therefore, the area of an inscribed equilateral triangle is 27√3 cm2.

### How do you solve an inscribed 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 inscribed angle formula?

Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of the intercepted arc. That is, m∠ABC=12m∠AOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.

How do you find the area of a right triangle inside a circle?

Approach: Formula for calculating the inradius of a right angled triangle can be given as r = ( P + B – H ) / 2. And we know that the area of a circle is PI * r2 where PI = 22 / 7 and r is the radius of the circle. Hence the area of the incircle will be PI * ((P + B – H) / 2)2.

#### What is the area of the shaded part?

The area of the shaded region is the difference between the area of the entire polygon and the area of the unshaded part inside the polygon. The area of the shaded part can occur in two ways in polygons. The shaded region can be located at the center of a polygon or the sides of the polygon.

#### How do you find the area of a shaded part?

Calculate the area of both shapes. The area of a rectangle is determined by multiplying its length times its width. The area of a circle is Pi (i.e., 3.14) times the square of the radius. Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape.

How do you visualize a circle in 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 make an equilateral triangle inside a circle?

Draw the first side. Use a ruler or the straight edge of your protractor to trace a straight line segment of an appropriate length.

• Use a protractor to measure a 60° angle at one end.
• Trace the second side. Measure out a new line segment that is equal in length to the first.
• Finish the triangle.
• ## How many triangles are in a circle?

There are 10 points lie on a circle. By joining points how many triangle can be drawn from these points? All 10 points on the circle are non collinear. For a triangle to be formed, we need 3 non collinear points. 10C3= 10!/7!3!= 120. Therefore, 120 triangles can be formed.

What is the difference between a circle and triangle?

is that triangle is (geometry) a polygon with three sides and three angles while circle is ( lb) a two-dimensional geometric figure, a line, consisting of the set of all those points in a plane that are equally distant from another point. to travel around along a curved path. Other Comparisons: What’s the difference?