Question

In the figure, if chords AB and CD of the circle intersect each other at right angles, then $x+y=$

• A. ${45}^o$
• B. ${60}^o$
• C. ${75}^o$
• D. ${90}^o$

Answer 1

The correct option is D

${90}^o$

In the circle, AB and CD are two chords which intersect each other at P at right angle i.e. $\angle CPB={90}^o$.

$\angle CABand\angle CDB$ are in the same segment.

$\therefore \angle CDB=\angle CAB=x$

Now, in $\Delta PDB$, Ext. $\angle CPB=\angle D+\angle DBP$

$\Rightarrow {90}^o=x+y(\because CD\perp AB)$

Hence, $x+y={90}^o$