R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: Exercise 7B

In the given figure, $\mathrm{\Delta ODC}~\mathrm{\Delta OBA}, \angle \mathrm{BOC}=115°$ and $\angle \mathrm{CDO}=70°$.
Find $\angle \mathrm{DCO}$.

In the given figure, $\mathrm{\Delta ODC}~\mathrm{\Delta OBA}, \angle \mathrm{BOC}=115°$ and $\angle \mathrm{CDO}=70°$.
Find $\angle \mathrm{OAB}$.

In the given figure, $\mathrm{\Delta ODC}~\mathrm{\Delta OBA}, \angle \mathrm{BOC}=115°$ and $\angle \mathrm{CDO}=70°$.
Find  $\angle \mathrm{OBA}$.

In the given figure, $\Delta OAB~\Delta OCD$. If $AB=8 \mathrm{cm}, BO=6.4 \mathrm{cm}, OC=3.5 \mathrm{cm}$ and $CD=5 \mathrm{cm}$, find $DO.$

In an isosceles $\Delta ABC$, the base $AB$ is produced both ways in $P$ and $Q$ such that
$AP\times BQ=A{C}^2.$
Prove that $\Delta ACP~\Delta BCQ.$

In a circle, two chords $AB$ and $CD$ intersect at a point $P$ inside the circle. Prove that $PA. PB= PC.PD$

Two chords$AB$and $CD$of a circle intersect at a point$P$ outside the circle.
Prove that: $PA. PB=PC.PD$

In a right triangle $ABC$, right angled at $B, D$ is a point on hypotenuse such that $BD\perp AC$ ,if $DP\perp AB$ and $DQ\perp BC$ then prove that
$D{P}^2=DQ.AP$