Lesson 6 Circle Challenges Practice Understanding

Ready

Find the perimeter of each polygon.

1.

2.

3.

4.

Set

5.

Write the equation of circle $Q$ .

6.

The point $(1, 1)$ is the center of a circle with a radius of $3$ . Does the point $(- 1, 3)$ lie inside, outside, or on the circle? Explain your answer.

7.

The diameter of a circle measures $16$ units and the center is at the intersection of $y_{1} = x + 7$ and $y_{2} = 2 x - 5$ . Prove that the equation of the circle is ${(x - 12)}^{2} + {(y - 19)}^{2} = 64$ .

8.

Triangle $W X R$ is inscribed in $⨀ Q$ . Segment $W R$ passes through the center of $⨀ Q$ and $\overset{―}{W R} ∥$ to the $x$ -axis. All $3$ vertices of $△ W X R$ lie on the circle. Use the information in the diagram to write the equation of $⨀ Q$ . Justify that your equation is correct.

9.

A circle lies in Quadrant II, tangent to $x = - 12$ and $x = - 4$ and the $x$ -axis. Find the center and radius of the circle. Then write the equation of the circle.

10.

Three points on a circle are $(- 8, 5)$ , $(3, - 6)$ , and $(14, 5)$ . Draw a diagram to explain why the equation of the circle is ${(x - 3)}^{2} + {(y - 5)}^{2} = 121$ .

11.

Complete the square to find the center and radius of a circle defined by the equation $x^{2} + y^{2} + 6 x - 10 y = 16$ .

12.

Complete the square to find the center and radius of a circle defined by the equation $x^{2} + y^{2} - 2 x - 12 y = 27$ .

Go

Fill in the number that completes the square. Then write the trinomial as the square of a binomial.

13.

$x^{2} + 6 x +$

Factored form:

14.

$x^{2} - 14 x +$

Factored form:

15.

$x^{2} - 50 x +$

Factored form:

16.

$x^{2} - 28 x +$

Factored form:

17.

$x^{2} - 11 x +$

Factored form:

18.

$x^{2} + 7 x +$

Factored form:

19.

$x^{2} + 15 x +$

Factored form:

20.

$x^{2} + \frac{2}{3} x +$

Factored form: