The circumcentres of four triangles are joined to form a
quadrilateral. What do you notice about this quadrilateral as the
dynamic image changes? Can you prove your conjecture?
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.
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
At the time of writing the hour and minute hands of my clock are at
right angles. How long will it be before they are at right angles
X is a moveable point on the hypotenuse, and P and Q are the feet
of the perpendiculars from X to the sides of a right angled
triangle. What position of X makes the length of PQ a minimum?
It is impossible to trisect an angle using only ruler and compasses
but it can be done using a carpenter's square.
Can you decide whether two lines are perpendicular or not? Can you
do this without drawing them?
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. . . .
Position the lines so that they are perpendicular to each other.
What can you say about the equations of perpendicular lines?
Find the area of the shaded region created by the two overlapping
triangles in terms of a and b?