Lesson 1 Circling Triangles Develop Understanding

Ready

Factor.

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Set

10.

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

Circle A with right triangles with hypotenuse = 8. xy

11.

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

Circle B with right triangles with hypotenuse = 3. xy

12.

Point is centered at the origin and is the midpoint of . Write an equation of a circle that passes through points and and has at its center.

Given: .

Coordinate axis with Coordinate C (0,0), right triangles in Quadrant I and III share Point C and WN=40. xy

13.

Write the equation of a circle that passes through the point and is centered at the origin.

14.

Write the equation of a circle that passes through the point and is centered at the origin.

15.

Let point be .

  • Draw a circle centered at the origin that passes through point . 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 and . Label the points on the circle.

  • Write the equation of the circle.

a blank 17 by 17 grid

Go

Each arc is shown in blue.

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

16.

Given: and

Find in radians.

Circle C with inscribed angle ACB

17.

Given: and

Find in radians.

Circle M with inscribed angle LMN

18.

Given: and

Find in radians.

Circle F with inscribed angle EFG

19.

Given: and

Find in radians.

Circle R with inscribed angle PRQ

20.

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