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Collinear and Equal Angles (Posted on 2013-11-09) Difficulty: 5 of 5
Let Γ1 and Γ2 be arbitrary circles that intersect at points P and Q.

Prove or disprove that there exist points M and N such that

(1) M ∈ Γ1\{P,Q},
(2) N ∈ Γ2\{P,Q},
(3) M, N, and P are collinear, and
(4) ∠MQP = ∠NQP.

If they exist, prove or disprove that they can be constructed with
straightedge and compass.

Here is a link to Wolfram MathWorld:
Definition of Set Difference

See The Solution Submitted by Bractals    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 3 of 5 |
(In reply to Solution by Harry)

1) In your proof you have /MPR = /NPS (which it is), but don't you have to show that S lies on PR?


2) Putting your construction on Geometer's Sketchpad everything works out. But, it seems that you have R and S on opposite sides of line PQ. Did you try your proof when R and S are on the same side of line PQ?

  Posted by Bractals on 2013-11-14 01:26:09
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