Lesson 4 Circling Triangles Develop Understanding

Ready

Factor.

1.

$b^{2} - 49$

2.

$b^{2} - 2 b + 1$

3.

$b^{2} + 10 b + 25$

4.

$x^{2} - y^{2}$

5.

$9 x^{2} - 66 x y + 121 y^{2}$

6.

$25 x^{2} - 49 y^{2}$

7.

$36 x^{2} + 60 x y + 25 y^{2}$

8.

$81 a^{2} - 16 d^{2}$

9.

$144 x^{2} - 312 x y + 169 y^{2}$

Set

10.

Circle $A$ is centered at the origin. Each of the four right triangles inside $⨀ A$ has a hypotenuse that measures $8 units$ . Write the equation of $⨀ A$ .

11.

Circle $B$ is centered at the origin. Each of the four right triangles inside $⨀ B$ has a hypotenuse that measures $3 units$ . Write the equation of $⨀ B$ .

12.

Point $C$ is centered at the origin and is the midpoint of $\overset{―}{W N}$ . Write an equation of a circle that passes through points $N$ and $W$ and has $C$ at its center.

Given: $W N = 40 units$ .

13.

Write the equation of a circle that passes through the point $(- \sqrt{7}, \sqrt{21})$ and is centered at the origin.

14.

Write the equation of a circle that passes through the point $(3 \sqrt{5}, - 6)$ and is centered at the origin.

15.

Let point $P$ be $(3, - 4)$ .

Draw a circle centered at the origin that passes through point $P$ . Use the Pythagorean theorem to identify three additional points in each of the Quadrants I, II, and III that lie on the circle and do not contain the numbers $3$ and $4$ . Label the points on the circle.
Write the equation of the circle.

Go

Each arc is shown in blue.

Each indicated angle is the central angle that intercepts the given arc.

16.

Given: $r = 4 inches$ and $\overset{⌢}{A B} = \frac{8 π}{3} inches$

Find $m ∠ B C A$ in radians.

17.

Given: $r = 10 m$ and $\overset{⌢}{N L} = \frac{15 π}{2} m$

Find $m ∠ L M N$ in radians.

18.

Given: $r = 18 cm$ and $\overset{⌢}{G E} = 21 π cm$

Find $m ∠ G F E$ in radians.

19.

Given: $r = 27 yd$ and $\overset{⌢}{P Q} = 3 π yd$

Find $m ∠ P R Q$ in radians.

20.

Each radius and arc length includes a unit such as feet or meters. Explain why radian measures do not include a unit.