Question

Which is the smallest of all the chords of a circle passing through a given point in it?

• A. Chord trisected at the point.
• B. Chord bisected at the point.
• C. Chord passing through the centre.
• D. Both (A)and (B)

Answer 1

The correct option is B Chord bisected at the point.

Let $C$ $(O,r)$ is a circle and let M is a point within it where O is the centre and r is the radius of the circle.
Let CD is another chord passes through point M.
We have to prove that $AB<CD$.
Now join OM and draw OL perpendicular to CD.
In right angle triangle $OLM$,
OM is the hypotenuse.
So $OM>OL$
$\Rightarrow$ chord CD is nearer to O in comparison to AB.
$\Rightarrow$ $CD>AB$
$\Rightarrow$ $AB<CD$

$\Rightarrow$ Smallest one is the one bisected at the point.