lines across the extremities of the two diameters. Observe that a square is formed
inside the circle.
- Regular Octagon in a Circle
Cut a sheet of paper in the form of a circle. Fold the paper twice so that two
diameters cutting at right angles are formed. Fold the paper again twice so that the
four right angles formed are further halved into eight angles of 45o each. Now fold
the paper eight times so that all the extremities of the diameters are connected.
Observe that a regular octagon is formed inside the circle.
- In a cyclic Quadrilateral the exterior angle is equal to the interior opposite angle
Construct a cyclic quadrilateral in a sheet of paper. Extend any one of the sides of the
quadrilateral beyond the circumference of the circle. Observe that an angle, called
exterior angle is formed between the side extended and one of the chords. Now cut
off the exterior angle from the cyclic quadrilateral. Place the part cut off coinciding
with the interior opposite angle and observe that the exterior angle is equal to the
interior opposite angle. That is angle BCE is equal to angle DAB.
G
H
I
A B C E F A E
B
D C
