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## Homework Statement

As shown in the diagram below, the shape consists of a square and a circle with centre Q. Given that QM = 3 cm, prove that MN = 6 cm.

Known data:

-- triangles APB and BQC are congruent

-- angle BMC = 90

-- triangles BMQ and BNA are similar and right-angled

2. Homework Equations

3. The Attempt at a Solution

2. Homework Equations

3. The Attempt at a Solution

This is a part of a structured question and I've already proved all the data listed above. I also know that AN = 6 cm as the triangles are similar, and I think that the solution might have something to do with triangle AMN being isosceles (but I can't prove that). There's probably something obvious I'm missing, so a nudge in the right direction would be greatly appreciated.