Q15 from Senior Mathematical Challenge 2018: A square is inscribed in a circle of radius 1. An isosceles triangle is inscribed in the square. What is the ratio of the area of this triangle to the area of the shaded region? (Requires Diagram))
Radius = 1, therefore diameter = 2Let x be the length of one side of the square.Using Pythagoras,x2 + x2 = 222x2 = 4x = sqrt(2)Area of isosceles triangle = side of square * half side of square= sqrt(2) * sqrt(2)/2= 1Shaded area = area of circle - area of square= π(1)2 - sqrt(2)2 = π - 2 Answer = 1:π-2
TH
Related Maths A Level answers
All answers ▸Integrate the function f(x)=lnx
two balls of similar size masses m and 2m are moving at speeds u and 2u along a frictionless plane, they collide head on and are reflected, assuming that the coefficient of restitution of this collision is 1, what the speeds are afterwards in u
How do you prove that (3^n)-1 is always a multiple of 2?
If y = (1+3x)^2, what is dy/dx?