Question

If $\stackrel{⌢}{AB}$ $\cong$ $\stackrel{⌢}{CD}$ then

• A. $\angle 1=\angle 2$
• B. $\angle 3=\angle 4$
• C. $\angle 2=\angle 3$
• D. None of these

Answer 1

The correct option is C $\angle 2=\angle 3$

Given: $\stackrel{⌢}{AB}$ $\cong$ $\stackrel{⌢}{CD}$
Hence, $\angle 1=\angle 4$ (Angles formed at the centre of the circle by equal segments)
Now, in $△OAC$
$OA=OC$
hence, $\angle OAC=\angle OCA$ (isosceles triangle property)
Hence, $\angle 2=\frac{180-\angle 1}{2}$ (Angle sum property) (1)
Similarly, In $△OBD$
$\angle 3=\frac{180-\angle 4}{2}$ (2)
Since, $\angle 1=\angle 4$
then, $\angle 2=\angle 3$ (from 1 and 2)