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
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
Three circular medallions fit in a rectangular box. Can you find the radius of the largest one?
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.
What is the value of r/ R?