A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
In the diagram below, a right-angled triangle has a line descending from its right angle, perpendicular to the hypotenuse.
If the hypotenuse length is 100cm, and if the line splits the base into 36cm and 64cm parts, what are the side lengths of the original right-angled triangle?