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Right Angled Possibilities

Weekly Problem 23 - 2007
If two of the sides of a right-angled triangle are 5cm and 6cm long, how many possibilities are there for the length of the third side?

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Incentre Angle

Weekly Problem 1 - 2011
Use facts about the angle bisectors of this triangle to work out another internal angle.

Bisector Intersection

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

(Diagram not to scale.)
In the triangle $PQR$, the angle $QPR=40^{\circ}$ and the internal bisectors of the angles at $Q$ and $R$ meet at $S$, as shown. What is the size of angle $QSR$?


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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