Question

What is the area of the shaded segment (in cm²), if the chord is a side of the maximum possible square that can be inscribed in
the circle? (Take pi = 22/7)
options
14
28
44
49​

Answer 1

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Answer 2

Answer:

Area of segment is $28.$

Step-by-step explanation:

Given, In problem figure, chord of circle is $14cm.$ And it is also the one side of maximum possible square that can be inscribed the circle of radius $r.$

Since, chord is side of a square.

Therefore, angle made by the chord at center is $90$°.

Since, base and height of the right triangle are same as $'r'.$

So, $\sqrt{r^2+r^2} =14$

             $\sqrt{2} r=14$

                 $r=\frac{14}{\sqrt{2}} cm$

So, Area of ssector $=(90$°$/360$°$)$ × $(\frac{22}{7} )$ × $r^{2}$

Now, area of triangular part $=\frac{1}{2} r^2$

So, area of segment

                    $=(\frac{22}{28} )r^{2} -(\frac{r^2}{2} )$

                    $=r^2(\frac{11}{14} -\frac{1}{2} )$

                    $=[r^2(22-14)]/28$

                    $=8r^2/28$

                    $=2r^2/7$

                    $=(2*14*14)/14$

                    $=28.$