Question

In the given circle with centre ‘O’, the mid – points of two equal chords $AB$ & $CD$ are $K$ & $L$ respectively.



If $\angle OLK={25}^{\circ }$,then $\angle LKB=$?

• A. ${125}^{\circ }$
• B. ${115}^{\circ }$
• C. ${105}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${115}^{\circ }$

O is the centre of circle. K and L are midpoints of Chords AB and CD respectively.



$\therefore OK\perp ABandOL\perp CD$
As $AB=CD$ [Given]
$\therefore AK=CL$ [midpoints of equal chords]
$\therefore OK=OL$ $\because \left(equalchordsareequidistantfromcentre\right)$
So $\Delta OKL$ is an isosceles triangle
$\therefore \angle OKL=\angle OLK={25}^{\circ }$ (given)
$\therefore \angle LKB=\angle OKL+\angle OKB={25}^{\circ }+{90}^{\circ }={115}^{\circ }$