Inscribed Circles (Handout J)

Front

What is an inscribed circle?

Back

An inscribed circle is a circle that is drawn inside a polygon such that it touches all the sides of the polygon. The center of the inscribed circle is called the incenter.

Front

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

Back

The radius (r) of the inscribed circle can be found using the formula: r = A/s, where A is the area of the triangle and s is the semi-perimeter.

Front

What is the formula for the circumference of a circle?

Back

The circumference (C) of a circle is calculated using the formula: C = 2πr, where r is the radius.

Front

If the radius of an inscribed circle is 7, what is the circumference?

Back

C = 2πr = 2 * 3.14 * 7 = 43.96.

Front

What is the semi-perimeter of a triangle?

Back

The semi-perimeter (s) of a triangle is half the sum of the lengths of its sides: s = (a + b + c) / 2.

Front

How do you calculate the area of a triangle?

Back

The area (A) of a triangle can be calculated using the formula: A = 1/2 * base * height.

Front

What is the relationship between the area and the radius of an inscribed circle?

Back

The area of a triangle can also be expressed as A = r * s, where r is the radius of the inscribed circle and s is the semi-perimeter.

Front

What is the value of π (pi) used in calculations?

Back

The value of π (pi) is approximately 3.14.

Front

If the circumference of a circle is 87.9 inches, what is the radius?

Back

Using the formula C = 2πr, the radius r can be found as r = C / (2π) = 87.9 / (2 * 3.14) ≈ 14.

Front

What is the formula for the area of a circle?

Back

The area (A) of a circle is calculated using the formula: A = πr².