Circles/Pythagorean Theorem Review

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

If a right triangle has legs of lengths 3 cm and 4 cm, what is the length of the hypotenuse?

Back

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the radius of a circle?

Back

The radius of a circle is the distance from the center of the circle to any point on its circumference.

Front

What is the diameter of a circle?

Back

The diameter of a circle is twice the length of the radius. It is the longest distance across the circle, passing through the center.

Front

How do you find the circumference of a circle?

Back

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

Front

What is the area of a circle?

Back

The area (A) of a circle can be calculated using the formula A = πr², where r is the radius.

Front

If the radius of a circle is 6 cm, what is its area?

Back

The area is 36π cm² (Using the formula A = πr²: A = π(6)² = 36π).

Front

What is a chord in a circle?

Back

A chord is a line segment with both endpoints on the circle.

Front

What is the relationship between the radius and the diameter?

Back

The diameter is twice the length of the radius (d = 2r).

Front

If a circle has a diameter of 10 cm, what is its radius?

Back

5 cm (Radius is half of the diameter: r = d/2 = 10/2 = 5).