10th Class Mathematics Areas Related to Circles Question Bank Area of Circle

  • question_answer
    A circle is inscribed is an equilateral triangle. If the in-radius is 21 cm, what is the area of the triangle?

    A)  \[1100\sqrt{3}\,c{{m}^{2}}\]              

    B)  \[1323\sqrt{3}\,c{{m}^{2}}\]  

    C)  \[1369\sqrt{3}\,c{{m}^{2}}\]              

    D)  \[1442\sqrt{3}\,c{{m}^{2}}\]

    Correct Answer: B

    Solution :

    (b): Centre of the circle lies on the median. If ?a? is side of equilateral \[\Delta le\], median \[=\frac{a\sqrt{3}}{2}\]       In - radius \[=\frac{a\sqrt{3}}{2}\times \frac{1}{3}=\frac{1}{2\sqrt{3}a}a=21\] \[\Rightarrow \]\[a=42\sqrt{3}\] Now find area \[=\frac{\sqrt{3}}{4}{{a}^{2}}\]  


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