Extension of Inscribed Angle Theorem

Q. In the given figure, chord ED is parallel to the diameter AC of the circle. Given, $\angle CBE={65}^{\circ }$, find $\angle DEC$.

1. ${35}^{\circ }$
   
2. ${115}^{\circ }$
3. ${25}^{\circ }$
4. ${15}^{\circ }$

Q. In Figure, $XY$ and $X^{\prime }{Y}^{\prime }$ are two parallel tangents to a circle with centre $O$ and another tangent $AB$ with point of contact $C$ intersecting $XY$ at $A$ and $X^{\prime }{Y}^{\prime }$ at $B$. Prove that $\angle$$AOB$$={90}^o$.

Q. In the given figure AC is the diameter of the circle with centre O. Chord BD is perpendicular to AC. Express p in terms of x.

1. $x/2$
2. ${90}^{\circ }+x/2$
3. ${90}^{\circ }-x/2$
4. ${180}^{\circ }-x$