Math Is Fun Forum

Strangerrr

Member

Registered: 2018-07-28

Posts: 23

Circles: Chords, Radii, and Arcs

I need help checking if my answers are correct.

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?

D4

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?

E 60 deg

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

14. What is the measure of arc BC?

D120 deg

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circles: Chords, Radii, and Arcs

hi Strangerrr

It's a property of all circumcircles that have one side as a diameter, that the angle made at the circumference is 90.

http://www.mathisfunforum.com/viewtopic.php?id=17799 post number 6.

So B = 90.

If you sketch the diagram and making BC a mirror line, reflect A and C in the mirror to get A' and C.

A'C = AC so CAA' is isosceles, and angle ACB = A'CB = 30, so ACA' = 60.  This makes triangle CAA' an equilateral triangle  with sides of 8.

That should help you do get the answers to these.

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

Strangerrr

Member

Registered: 2018-07-28

Posts: 23

Re: Circles: Chords, Radii, and Arcs

Thank you for helping!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circles: Chords, Radii, and Arcs

hi Strangerrr

It was a pleasure to 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