Unit 7 Circles Retest

Front

What is the standard form of a circle's equation?

Back

The standard form of a circle's equation is (x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.

Front

How do you convert the general equation of a circle to standard form?

Back

To convert the general equation of a circle (Ax² + Ay² + Bx + Cy + D = 0) to standard form, complete the square for the x and y terms.

Front

What is the relationship between a tangent and a radius at the point of tangency?

Back

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Front

If a point is outside a circle, how do you find the length of the tangent from that point to the circle?

Back

Use the Pythagorean theorem: if the distance from the point to the center is d and the radius is r, then the length of the tangent is √(d² - r²).

Front

What is the radius of a circle if a point is 17 cm from the center and the tangent to the circle at that point is 15 cm?

Back

The radius is 8 cm, calculated using the Pythagorean theorem: r = √(17² - 15²).

Front

What is the formula for the circumference of a circle?

Back

The circumference C of a circle is given by the formula C = 2πr, where r is the radius.

Front

What is the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Front

How do you find the perimeter of a triangle given its side lengths?

Back

The perimeter P of a triangle is the sum of the lengths of its sides: P = a + b + c.

Front

What is the relationship between the angles in a triangle?

Back

The sum of the interior angles in a triangle is always 180 degrees.

Front

What is the equation of a circle with center (-3, 6) and radius 5?

Back

The equation is (x + 3)² + (y - 6)² = 25.