Triangles

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

Is it possible to find the angles in this rather special isosceles triangle?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?