Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

This article is about triangles in which the lengths of the sides and the radii of the inscribed circles are all whole numbers.

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. . . .

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.

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

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

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Triangle ABC has altitudes h1, h2 and h3. The radius of the inscribed circle is r, while the radii of the escribed circles are r1, r2 and r3 respectively. Prove: 1/r = 1/h1 + 1/h2 + 1/h3 = 1/r1 +. . . .

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.

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

Take any point P inside an equilateral triangle. Draw PA, PB and PC from P perpendicular to the sides of the triangle where A, B and C are points on the sides. Prove that PA + PB + PC is a constant.

If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

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

Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Which of these triangular jigsaws are impossible to finish?