Math Is Fun Forum

nikita

Member

Registered: 2016-05-22

Posts: 1

Geo Circles

(1)  The ratio of three consecutive angles in a cyclic quadrilateral is $2:3:4$. Find the largest angle of the quadrilateral, in degrees.

(2)  Points $A$ and $B$ are on circle $O$ such that arc $AB$ is 80 degrees. A circle is constructed that passes through $A$, $B$, and $O$. Find the measure of arc $AOB$ on this circle.

(3)  In the diagram, $\angle A = 30^\circ$, $\overarc{DE} = 170^\circ$, and $\overarc{BC} = 110^\circ$. Find the measure of arc $CE$, in degrees.
http://latex.artofproblemsolving.com/6/5/3/6531e7a7ad5a4a9b605acf38834256bf2a4cc45d.png

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geo Circles

For3. Diagram is not reachable.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geo Circles

Here is the diagram for 3)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geo Circles

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Geo Circles

hi nikita,

In the instruction page for asking for help it says "We are happy to help! But we don't do your homework for you."

I thin that applies to AoPS problems too.

So, if I help, I try to provide hints to the method rather than just posting an answer.  If you would like such hints please post again and I'll do so.

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