Properties of Radical Axis

Q. Given circle with centre $O$ and $BC\parallel ED$, $m\left(arcBC\right)={94}^0$, $m\left(arcED\right)={86}^0$, $\angle ADE=8^0$. The m$\left(arcEB\right)$ is :

1. ${47}^o$
2. ${120}^o$
3. ${90}^o$
4. ${16}^o$

Q. In the given figure (not to scale) O is the centre of the circle $\overline{AC}$ and $\overline{BD}$ intersect at P. PB = PC $\angle PBO={25}^{\circ }$ and $\angle BOC={130}^{\circ }$ then find $\angle ABP+\angle DCP$

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${15}^{\circ }$
4. None of these

Q. The focus of the centers of the circle such that the point (2, 3) is the mid point of the chord 5x+2y=16 is:

1. 2x-5y+11=0
2. 2x+5-11=0
3. 2x+5y+11=0
4. 2x-5y-11=0