Question

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

(a) ${45}^{\circ }$

(b) ${60}^{\circ }$

(c) ${75}^{\circ }$

(d) ${90}^{\circ }$

Answer 1

The correct option is (d) 90°
We are given the following figure

$\angle ACD=\angle ABD$ (Angle in the same segment are equal)
$\Rightarrow ACD=y$

Consider the ΔACM in which
$\angle ACM+x+90=180$
$\Rightarrow \angle ACM+x+90=180$
$\Rightarrow y+x+90=180$ [Since, $\angle ACM=\angle ACD$]
$\Rightarrow x+y=180-90$
$\therefore x+y=90$

Hence, the correct answer is option (d).