1 out of 3
1 out of 3
The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ
1 out of 3
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
1 out of 3
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.
1 out of 3
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?
1 out of 3
A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?
1 out of 3
Can you calculate the length of this diagonal line?
2 out of 3
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
2 out of 3
ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
2 out of 3
Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...
