Geometry challenge


Part 1

Consider the angle on the circumference of the circle which is "standing" on the chord (subtended by the arc CD)

i. Describe the relationship between the "angle at the centre" and the angle "on the circumference" subtended by the same arc. (Angles, DAC and DEC) ii. Draw a line passing through A and E to help you 'prove" the observation you made in part i...

Now consider the situation shown below.

iii. What can you deduce about the two angles on the circumference of the circle, and why? Hint: measure the angles...!

Part 2

In the diagram below O is the centre of the inscribed circle of the triangle ABC. The line AO is produced to meet the circumcircle at X.

PROVE that X is equidistant from B, O and C.