question_answer

Assertion (A): Area of the square inscribed in a circle of radius r is \[2{{r}^{2}}\,sq.\] units.

Reason (R): Area of the major segment of a circle = area of the circle - Area of minor segment.

A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)

B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)

C) Assertion (A) is true but Reason (R) is false

D) Assertion (A) is false but Reason (R) is true

Correct Answer: B

Solution :

[b] Given, r is the radius of circle and let a be the side of square inscribed in the circle.

In \[\Delta ABC,\]           \[\angle B=90{}^\circ \]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,(2{{r}^{2}})={{a}^{2}}+{{a}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,4{{r}^{2}}=2{{a}^{2}}\Rightarrow {{a}^{2}}=2{{r}^{2}}\]

\[\Rightarrow \]  Area of square \[={{a}^{2}}=2{{r}^{2}}sq.\] units

\[\therefore \]  Assertion: True; Reason: True but it is not the correct explanation of Assertion.