A place I would like to share some concepts, ideas, puzzles that simulate the minds of those interested in Math - for competitions or fun.
Tuesday, January 03, 2012
Puzzle 20 - Three circles
are three circles.
Centre of lies on . touch internally. and cut at A and B. AB is extended to cut at X and Y. and touch at M.
M is joined to X and Y. MX and MY cut at P and Q.
Prove that PQ is a tangent to .
I think the solution I have for this problem is little long. I am looking for simpler solution.
dear teacher; I am nasser Ali how are you I see that c1, c2,and c3 must collinear because c2c3 is the axis of symmetre of AB and AB is a chored in c1 then,it must passes through c1,but the figure not give that.tell me if I am right or not to complete solution thank you my teacher.
5 comments:
Unable to understand the puzzle. I think some text is missing. Is it possible to give a figure for the puzzle?
dear teacher;
I am nasser Ali
how are you
I see that c1, c2,and c3 must collinear because c2c3 is the axis of symmetre of AB and AB is a chored in c1 then,it must passes through c1,but the figure not give that.tell me if I am right or not to complete solution
thank you my teacher.
Iam sorry .i am not right
Centers need not be collinear. Check
the figure.
i remember this appeared in international olympiad 1999
by taking two coaxial circles this can be done using coordinate geomtry easily
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