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

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

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.

What is the radius of a circle 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 find the radius of a circle with the area of a triangle?

Hint: use the fact that the area A (of the triangle) is given by: A=pr2 where p is the perimeter and r the incircle radius. This formula can easily be proved ( divide the triangle in three triangle with a common vertex at O) and is valid for a convex polygon..

### How do we find the radius of a circle?

How do you find the radius of a circle?

1. Radius of a circle from area: if you know the area A , the radius is r = √(A / π) .
2. Radius of a circle from circumference: if you know the circumference c , the radius is r = c / (2 * π) .
3. Radius of a circle from diameter: if you know the diameter d , the radius is r = d / 2 .

How do you find the radius of a circle using the Pythagorean Theorem?

So now we have our Pythagorean Theorem equation: x^2 + y^2 = r^2. This is also the equation for a circle centered on the origin on the coordinate plane. [The more general equation for a circle with a center (a,b) is (x-a)^2 + (y-b)^2 = r^2.

How do you find the radius?

Just remember to divide the diameter by two to get the radius. If you were asked to find the radius instead of the diameter, you would simply divide 7 feet by 2 because the radius is one-half the measure of the diameter. The radius of the circle is 3.5 feet. You can also use the circumference and radius equation.

## How do you find the radius of a circle inside a circle?

To calculate the radius of a circle by using the circumference, take the circumference of the circle and divide it by 2 times π. For a circle with a circumference of 15, you would divide 15 by 2 times 3.14 and round the decimal point to your answer of approximately 2.39. Be sure to include the units in your answer.

How do you find the radius and area of a circle inscribed?

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A=πr2 .

What is the radius of a right angle?

To find the area of a circle inside a right angled triangle, we have the formula to find the radius of the right angled triangle, r = ( P + B – H ) / 2. Given the P, B and H are the perpendicular, base and hypotenuse respectively of a right angled triangle. where π = 22 / 7 or 3.14 and r is the radius of the circle.

### How do you find the circumference of a circle with a right 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.

How do you solve for radius and diameter?

To find the radius from the circumference of a circle, you have to do the following:

1. Divide the circumference by π, or 3.14 for an estimation. The result is the circle’s diameter.
2. Divide the diameter by 2.
3. There you go, you found the circle’s radius.

How to find the radius of incircle of a triangle?

You can check it with taking different sets of examples. Radius of incircle =area of triangle/s. Where s= (a+b+c)/2. 5cm. Find the radius of incircle. Area of right triangle= (3.4)/2=6cm^2.

## How do you find the radius of a circle with sides?

First add the two smaller sides. Now subtract the longer side from the sum you got in step 1. Finally divide the above result by 2. For example: say you need to find the radius of the circle inscribed in a right triangle with sides 5 cm, 12 cm and 13 cm.

What is the inradius of a right angled triangle having sides?

Every right angled triangle have their sides in the ratio 3:4:5 (base: height: hypotenuse), let k be the proportional constant So in general we can conclude that inradius (r) of a right angled triangle having sides a, b, c ( i.e length, breath, hypotenuse) respectively= k = a/3 = b/4 = c/5 You can check it with taking different sets of examples.

How do you find the area of a triangle?

You can easily calculate the area of the triangle. Then divide the triangle into three smaller ones: $AOB, BOC, COA$. Notice that their areas are respectively $AB\\cdot r/2, BC\\cdot r/2, CA\\cdot r/2$.