A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
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.
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.
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. . . .
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.
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. . . .
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
+. . . .
Jennifer Piggott and Charlie Gilderdale describe a free interactive
circular geoboard environment that can lead learners to pose
Prove that, given any three parallel lines, an equilateral triangle
always exists with one vertex on each of the three lines.
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.
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. . . .
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.
Find the area of the shaded region created by the two overlapping
triangles in terms of a and b?
This article is about triangles in which the lengths of the sides and the radii of the inscribed circles are all whole numbers.
From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.