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
I keep three circular medallions in a rectangular box in which they
just fit with each one touching the other two. The smallest one has
radius 4 cm and touches one side of the box, the middle sized one
has radius 9 cm and touches two sides of the box and the largest
one touches three sides of the box. What is the radius of the
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?