Question

In the given figure, AB is a diameter of the circle with centre O. DO is parallel to CB and $\angle$ DCB = ${120}^o$. Calculate :

(i) $\angle$ DAB, (ii) $\angle$ DBA,

(iii) $\angle$ DBC, (iii) $\angle$ ADC.

Also, show that the $\Delta$ AOD is an equilateral triangle.

Answer 1

(i) is a cyclic quadrilateral

(ii) (angle in the semicircle)

In ,

In

(iii)

(alternate angles)

(iv)

(cyclic quadrilateral)

In ,

(Radius of the same circle)

Therefore all angles are . Hence is an equilateral triangle.