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

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

Click the figure below to enlarge the problem 948.

## Saturday, December 21, 2013

### Geometry Problem 948: Intersecting Circles, Secant, Cyclic Quadrilateral, Concyclic Points

Labels:
concyclic,
cyclic quadrilateral,
intersecting circles,
secant

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Let S(B, k, θ) be a homothetic rotation transformation,

ReplyDeletecentered at B, such that C₁→C₂, D₁→D₂.

Then ∠D₁C₁B=∠D₂C₂B.

Hence, BC₁FC₂ are concyclic.

To show that C2 and D2 are the image of C1 and D1 in the transformation S(B, k,θ) we need to show that ∠C1BC2=∠D1BD2 and BC2/BC1= BD2/BD1 .

DeletePeter Tran

∠D₁C₁B=∠D₁AB deoareceBD₁C₁A concyclic,∠D₁AB.+∠D₂AB=180=>∠D₂C₂B=∠D₁C₁B si BC₁FC₂ concyclic.

ReplyDeleteExternal angle at F = < FD1D2 + < FD2D1 = < ABC1 + < ABC2 = < C1BC2 and the result follows

ReplyDeleteSumith Peiris

Moratuwa

Sri Lanka