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#1 2017-07-28 04:20:21

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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#2 2017-07-28 04:47:35

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,109
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.

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#3 2017-07-28 22:45:57

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,139

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.

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


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#4 2017-07-29 10:57:53

DarkTangent
Member
Registered: 2017-07-03
Posts: 20

Re: Lengths and Angles in Circles

zetafunc wrote:

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.

bob bundy wrote:

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!


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

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