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Isosceles Seven
Age 14 to 16
Challenge Level 
You could start by considering a simpler case, such as the one below:
If angle $BAC = x$, what other angles can you find?
Can you find angle $ABC$ in terms of $x$?
Can you find angle $CBD$ in terms of $x$?...
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A Problem of Time
Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?
Quad in Quad
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Arrowhead
The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?