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At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

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No Right Angle Here

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

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A Sameness Surely

Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST and PU are perpendicular to AB produced. Show that ST + PU = AB

Triangle Split

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

In the diagram the length $SP$, $SQ$ and $SR$ are equal and the angle $SRQ$ is $x^\circ$. What is the size (in degrees) of the angle $PQR$?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.

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