M L Aggarwal Solutions for Chapter: Circles, Exercise 3: Exercise 10.3

In the adjoining figure, $I$ is the incentre of $∆\mathrm{ABC}$. $AI$ produced meets the circumcircle of $∆\mathrm{ABC}$ at $D$. If $\angle \mathrm{ABC}=52°$ and $\angle \mathrm{ACB}=78°$, find the measures of: $\angle BCD$.

In the adjoining figure, $I$ is the incentre of $∆\mathrm{ABC}$. $AI$ produced meets the circumcircle of $∆\mathrm{ABC}$ at $D$. If $\angle \mathrm{ABC}=52°$ and $\angle \mathrm{ACB}=78°$, find the measures of: $\angle CBD$.

In the adjoining figure, $I$ is the incentre of $∆\mathrm{ABC}$. $AI$ produced meets the circumcircle of $∆\mathrm{ABC}$ at $D$. If $\angle \mathrm{ABC}=52°$ and $\angle \mathrm{ACB}=78°$, find the measures of: $\angle DCI$.

In the adjoining figure, $I$ is the incentre of $∆\mathrm{ABC}$. $AI$ produced meets the circumcircle of $∆\mathrm{ABC}$ at $D$. If $\angle \mathrm{ABC}=52°$ and $\angle \mathrm{ACB}=78°$, find the measures of: $\angle BDC$.

In the adjoining figure, $I$ is the incentre of $∆\mathrm{ABC}$. $AI$ produced meets the circumcircle of $∆\mathrm{ABC}$ at $D$. If $\angle \mathrm{ABC}=52°$ and $\angle \mathrm{ACB}=78°$, find the measures of: $\angle BIC$.

Prove that a cyclic rhombus is a square.

In the adjoining figure, $ABC$ and $DEF$ are straight lines. Prove that $AD$ is parallel to $CF$.

In the adjoining figure, $ABC$ is an isosceles triangle in which $AB=AC$ and circle passing through $B$ and $C$ intersects sides $AB$ and $AC$ at points $D$ and $E$. Prove that $DE\left|\right|BC$.