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. . . .
Find the area of the shaded region created by the two overlapping
triangles in terms of a and b?
Two tangents are drawn to the other circle from the centres of a
pair of circles. What can you say about the chords cut off by these
tangents. Be patient - this problem may be slow to load.
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.
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.
A very mathematical light - what can you see?
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. . . .
A hexagon, with sides alternately a and b units in length, is
inscribed in a circle. How big is the radius of the circle?
From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Jennifer Piggott and Charlie Gilderdale describe a free interactive
circular geoboard environment that can lead learners to pose
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?
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.
Prove that, given any three parallel lines, an equilateral triangle
always exists with one vertex on each of the three lines.
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. . . .
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.