Geometry Problem. Post your solution in the comments box below.

Level: Mathematics Education, High School, Honors Geometry, College.

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## Tuesday, July 14, 2015

### Geometry Problem 1134: Tangent Circles, Tangent Line, Triangle, Circumcircle, Circumcenter

Labels:
circle,
circumcenter,
circumcircle,
tangent,
triangle

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Points A ,O1 and O2 are collinear

ReplyDeleteLets line joining A,O1 and O2 intersects BD at E and BC at F.

Lets assume angle AO2D = x

And angle AO1C = y

We can see that Angle BEF = 90 - x

And Angle BFE = y - 90

And we get Angle EBF = Angle DBC = 180 - (y-x)

Also Angle O1AC = 90 - y/2

Angle O1AD = 90 + (x/2)

We get angle DAC = 180 - [(y-x)/2]

Since O3 is circumcentre of triangle ACD

Angle DO3C = y - x

It means quad. BCO3D is cyclic and O3 lies on circle O4.