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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


As $\angle QPR=40^{\circ}$, $\angle PQR+\angle PRQ=180^{\circ}-40^{\circ} =140^{\circ}$.

So $\angle SQR+\angle SRQ=140^{\circ}/2=70^{\circ}$. Therefore $\angle QSR =180^{\circ}-70^{\circ}=110^{\circ}$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.