Math Is Fun Forum

DarkTangent

Member

Registered: 2017-07-03

Posts: 20

Lengths and Angles in Circles

Triangle

has a right angle at

,

, and

. Find the radius of the incircle of

.

Circle

is the incircle of

and is also the circumcircle of

. The point

is on

, the point

is on

, and the point

is on

. If

,

, and

, what is the measure of

?

Hi! I am in geometry and I have been working on these problems for a while. Please help!

Last edited by DarkTangent (2017-07-28 04:22:48)

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All our dreams can come true if we have the courage to pursue them - Walt Disney

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,440

Website

Re: Lengths and Angles in Circles

Hi DarkTangent,

I have fixed your LaTeX -- on this forum, you can type LaTeX inside [math] tags rather than dollar signs.

You can find some useful information here.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Lengths and Angles in Circles

hi DarkTangent

I find it best to get a really good diagram first.  I use some software called Sketchpad but you can also use geogebra which is free.

In the first question you can write an equation for DA in terms of ED, and then CD in terms of ED.  Add and re-arrange to get ED.

In the second you should be able to work out YOX.  The angle at the edge, YZX, is half this using angle properties of a circle.

Bob

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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

DarkTangent

Member

Registered: 2017-07-03

Posts: 20

Re: Lengths and Angles in Circles

Hi DarkTangent,

I have fixed your LaTeX -- on this forum, you can type LaTeX inside [math] tags rather than dollar signs.

You can find some useful information here.

Thanks! That helped a lot.

hi DarkTangent

I find it best to get a really good diagram first.  I use some software called Sketchpad but you can also use geogebra which is free.

http://i.imgur.com/QVbD1by.gif

In the first question you can write an equation for DA in terms of ED, and then CD in terms of ED.  Add and re-arrange to get ED.

In the second you should be able to work out YOX.  The angle at the edge, YZX, is half this using angle properties of a circle.

Bob

On it!

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All our dreams can come true if we have the courage to pursue them - Walt Disney