Question

Assertion: The radius of a circle is 10 cm and the length of one of its chords is 16 cm. Then, the distance of the chord from the centre is 6 cm.
Reason: The perpendicular from the centre of a circle to a chord (other than the diameter) bisects the chord.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(a) Both the assertion and the reason are true and the reason is a correct explanation of the assertion.
Assertion(A): Let O be the centre of a circle and AB be the chord. Draw OL ⊥ AB.
Then L is the mid point of AB.
Now, OA = 10 cm and AL = $\frac{1}{2}\mathrm{AB}=8\mathrm{cm}$

Thus, $\mathrm{OL}=\sqrt{{\mathrm{OA}}^2-{\mathrm{AL}}^2}=\sqrt{{\left(10\right)}^2-{\left(8\right)}^2}=\sqrt{36}=6\mathrm{cm}$
i.e., assertion(A) is true.
Clearly, reason (R) gives assertion (A).