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

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

Click the figure below to view the complete problem 1034.

## Tuesday, July 29, 2014

### Geometry Problem 1034: Triangle, Three equal Incircles, Tangent lines, Isoperimetric triangles, Equal perimeter

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Let the three tangent points of circle A2, start from A, anti-clockwise, be L, M, N.

ReplyDeleteLet the three tangent points of circle B2, start from B, anti-clockwise, be P, Q, R

Let the three tangent points of circle C2, start from C, anti-clockwise, be X, Y, Z.

Then

A2B2 = NP = NC1 + PC1 = MC1 + QC1

B2C2 = RX = RA1 + XA1 = QA1 + YA1

C2A2 = ZL = ZB1 + LB1 = MB1 + YB1

Hence, the result follows.