Math Is Fun Forum

alexxb

Member

Registered: 2016-05-27

Posts: 2

Circles: Chords, Radii, and Arcs

I try posting about this topic before but I got confuse with the site sorry

I would be grateful if someone would explain how to answer the following questions.
Thank you in advance!

[picture added bobbym]

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?

A8
B2
C10
D4
E 7
F 16

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

A90 deg
B25 deg
C30 deg
D120 deg
E 60 deg
F 72 deg

14. What is the measure of arc BC?

A20 deg
B45 deg
C75 deg
D120 deg
E 15 deg
F 90 deg

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?

A60 deg
B7.5 deg
C30 deg
D15 deg
E 90 deg
F 120 deg

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?

A18
B38
C6
D15
E 4
F 29

Bob

Administrator

Registered: 2010-06-20

Posts: 10,642

Re: Circles: Chords, Radii, and Arcs

hi alexxb

These problems all require the use of the angle properties of a circle together with Pythagoras' theorem.  You'll find a thread that deals with these here:

http://www.mathisfunforum.com/viewtopic.php?id=17799

Have a look and see if that's enough to help you out with these.  If you post your answers to those you can do, that'll give me a better idea of where you need help.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sca1een

Member

Registered: 2016-06-10

Posts: 1

Re: Circles: Chords, Radii, and Arcs

12. D >> AC = AB / sin 30 = 4 / 1/2 = 8; r = AC / 2 = 4
13. E >> let's name circle center D and DB = DA > ADB is an equilateral triangle with ABD = BAD = ADB = 60
14. D (similar to #13 but with isosceles triangle)
19. E >>I'm not sure but no matter where I put this point D, the angle seems always to be 90.
20. D >> AC = √BC 2 + AB 2= √ 900 = 30; r = 15

Last edited by sca1een (2016-06-23 20:10:25)