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Bendy Quad

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Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

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Get Cross

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

Raising the Roof

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

We have had a number of excellent solutions to this problem from Year 11 pupils in Sharnbrook School in Bedforshire. And they didn't all solve the problem in the same way...

Jennie, Emily, Peter and Hannah sent in this solution, and used Pythagoras' Theorem to find one of their answers.

Megan, Shivani, Will, Austen and Michael managed to find b in a different way, using what they knew about the angles in the roof.

Mollie, Meg and Jack also used Pythagoras, and relabeled the angles and sides to make it easier for them to answer the questions. Perhaps they should have returned to the original labels at the end of their solution...

Olivia, Alex and Toby sent in very clear solutions to the first and third parts of the problem. We'll assume that they could have also done the second part!