Question

Assertion (A)
In the given figyre, a quadrilateral ABCD is drawn to circumscribe a given circle, as shown.
Then, AB + BC = AD + DC.
Figure

Reason (R)
In two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

Answer 1

(d) Assertion (A) is false and Reason (R)is true.
Assertion (A) is false$[\text{Since}\mathrm{the}\mathrm{}\mathrm{correct}\mathrm{}\mathrm{result}\mathrm{}\mathrm{is}AB+CD=AD+BC]$
$$\begin{gathered} \mathrm{Since}\mathrm{}\mathrm{the}\mathrm{}\mathrm{length}\mathrm{}\mathrm{of}\mathrm{}\mathrm{tangents}\mathrm{}\mathrm{drawn}\mathrm{}\mathrm{from}\mathrm{an}\mathrm{external}\mathrm{}\mathrm{point}\mathrm{}\mathrm{are}\mathrm{}\mathrm{equal},\text{therefore}: \\ \mathrm{A}\mathrm{P}=\mathrm{A}\mathrm{S} \\ \mathrm{B}\mathrm{P}=\mathrm{B}\mathrm{Q} \\ \mathrm{C}\mathrm{Q}=\mathrm{C}\mathrm{R} \\ \mathrm{R}\mathrm{D}=\mathrm{S}\mathrm{D} \\ \therefore \mathrm{A}\mathrm{B}+\mathrm{C}\mathrm{D}=\left(\mathrm{A}\mathrm{P}+\mathrm{P}\mathrm{B}\right)+\left(\mathrm{C}\mathrm{R}+\mathrm{D}\mathrm{R}\right) \\ =\mathrm{A}\mathrm{S}+\mathrm{B}\mathrm{Q}+\mathrm{C}\mathrm{Q}+\mathrm{S}\mathrm{D} \\ =\left(\mathrm{A}\mathrm{S}+\mathrm{S}\mathrm{D}\right)+\left(\mathrm{B}\mathrm{Q}+\mathrm{C}\mathrm{Q}\right) \\ =\mathrm{A}\mathrm{D}+\mathrm{B}\mathrm{C} \end{gathered}$$