# Geometry : Right Triangle Inscribed in a Circle

Using the diagram attached:

11. What is the measure of arc AC?

12. If ABC is a 30-60-90 triangle, with angle ACB at 30 degrees, and line segment AC is the diameter of the circle, then if the length of line segment AB is 4, what is the radius of the circle?

13. Working with the information from 12 from here to #16, what is the measure of arc AB?

14. What is the measure of arc BC?

15. Are arcs ABC and AC equal?

16. What is the measure of chord BC?

17. If the measure of arc AB is 75 degrees, what is the measure of arc BC?

18. If the measure of arc AB is 80 degrees, what is the measure of angle CAB?

Hint: Remember that all the angles in a triangle add up to 180 degrees.

19. If I created an imaginary point on arc AC named D, and drew line segments from points A and C to D, what would the measure of angle ADC be?

20. If line segment BC has a length of 24, and line segment AB has a length of 18, what is the radius of the circle?

See attached file for full problem description.

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#### Solution Summary

Geometry questions about a right triangle inscribed in a circle are answered.