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Challenge 429: Twisted Triangles

These triangles might test your trigonometric talents!

Triangle ABC is equilateral with side length 14.

Triangle PQR is also equilateral with side length 4.

Triangle PQR is positioned inside triangle ABC such that A, P, Q lie on a straight line; B, Q, R lie on a straight line; C, R P lie on a straight line; and AP = BQ = CR.

What is the length AP?

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.