Question

The points A, B, C, D and E lie on a circle.
AD is a diameter of the circle.
DB bisects angle ADC.
Angle ADC = 56°.
(a) Giving your reasons, write down
(i) angle DCA,
(ii) angle DAC,
(iii) angle CBA,
(iv) angle AEB.
(b) It is given that EB is parallel to DC and that EB cuts AD at X.
[You must not assume that X is the centre of the circle.]
Show that triangle BDX is isosceles.
(c) Find angle EBA.
(d) Hence or otherwise show that X is the centre of the circle.

Answer 1

DCA is easy right?