Question

Two chords $AB$ and $CD$ of a circle are each at distance of $4$ cm from the centre. Then $AB$ = $CD$.

State true or false.

• A. True
• B. False
• C. Cannot be decided
• D. None of the above

Answer 1

The correct option is A True

Given- $AB\&CD$ are chords of a circle and they are equidistant (4cm) from the centre O.

To find out- Whether $AB=CD.$

Solution-

$OM$ and $ON$ are perpendiculars=4cm from O to $AB$ & $CD$, respectively.

$\therefore$ They bisect $AB$ & $CD$

i.e $AM=\frac{1}{2}AB$ & $DN=\frac{1}{2}DC$

$\angle OMA=\angle OND={90}^o.$

Now, between the $\Delta AOM$ & $△DON$ we have, $OM=ON=4$cm ...(given),

$\angle OMA=\angle OND={90}^o$

$OA=OD$ ...(radii of the same circle).

$\therefore \Delta AOM\equiv \Delta DON$ ...(RHS test).

$\therefore AM=DN⟹AB=DC.$

So, the statement is true.