Question

In the given figure,$AB$ and $CD$ are the diameters of circle and $O$ is the centre of the circle. Then, which of the following is correct ?

• A. $△AOD\cong △COB$
• B. $△ACB\cong △CAD$
• C. $\angle ADC=\angle CBA$
• D. All of the above

Answer 1

The correct option is D All of the above

In $△AOD$ and $△COB$
$AO=CO$ (radius)
$BO=DO$ (radius)
$\angle AOD=\angle COD\text{(vertically opp. angles)}$
So, $△AOD\cong △COB$ (SAS)

Now, $△ACB$ and $△CAD$
$\angle ACB=\angle CAD\text{(diameter make}{90}^o\text{at cirumference of circle)}$
$AB=CD$ (diameters of same circle)
$AC=CA$ (common side in both)
So, $△ACB\cong △CAD$ (Hypotenuse-Leg-Congruency

And $\angle ADC=\angle CBA\text{(angles made by chord AC)}$

As all are correct so, option $\left(d\right)$ correct.