| Assertion (A): In the figure, \[{{C}_{1}}\] and \[{{C}_{2}}\]are two circles with radii \[\text{7 cm}\] and \[\text{5 cm}\] respectively, then area of shaded portion is \[24\,\pi \,c{{m}^{2}}\] . |
| Reason (R): When two circles touch internally, the distance between their centres is equal to sum of their radii. |
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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: C
Solution :
| [c] Area of circle \[{{C}_{1}}=\pi {{(7)}^{2}}=49\pi c{{m}^{2}}\] |
| Area of circle \[{{C}_{2}}=\pi {{(5)}^{2}}=25\pi c{{m}^{2}}\] |
| Area of shaded portion = Area of circle \[{{C}_{1}}\]-Area of circle \[{{C}_{2}}\] |
| \[=49\pi -25\pi =24\pi c{{m}^{2}}\] |
| \[\therefore \] Assertion: True: Reason: False. |
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