Math Is Fun Forum

Oran2009

Member

Registered: 2016-06-13

Posts: 21

Circle Geometry Questions

I have some problems that I would like full solutions and answers.. Please help me quick!

1) Let

be twelve equally spaced points on a circle with radius 1. Find

(The sum includes the square of the distance between any pair of points, so the sum includes

2) Let

be a cyclic quadrilateral. Let

be the intersection of

and

, and let

be the intersection of

and

. Prove that the angle bisectors of

and

are perpendicular.

Please help me.

Last edited by Oran2009 (2016-06-30 07:34:19)

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Circle Geometry Questions

Last edited by thickhead (2016-07-08 21:05:25)

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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.}

ncyaclauds

Member

Registered: 2016-06-18

Posts: 8

Re: Circle Geometry Questions

I don't understand how you got <D + x + y = 90, from those three equations and I believe that you described the points wrong. did you mean G was the point where the two bisectors intersected?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Circle Geometry Questions

Now it stands corrected.

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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.}