You may also like

problem icon

Some(?) of the Parts

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

problem icon

Ladder and Cube

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?

problem icon

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

Round and Round

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

Circle inside semicircle

What percentage of the sector OAB is taken up with the inner circle?

Circle inside quarter circle

What happens if angle AOB is less than 90° or between 90 and 180 degrees?