You visited us 1 times! Enjoying our articles? Unlock Full Access!

Area of a Circle

If the sum of...

Question

If the sum of the areas of two circles with radii r₁ and r₂ is equal to the area of a circle of radius r, then $r_{1}^{2} + r_{2}^{2}$
(a) >r²

(b) =r²

(c) <r²

(d) None of these

Open in App

Solution

We have given area of the circle of radius r₁plus area of the circle of radius r₂ is equal to the area of the circle of radius r.

Therefore, we have,

Cancelling, we get

Therefore, .

Hence, the correct answer is option (b).

Suggest Corrections

Similar questions

If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

R_{1}

R_{2}

R_{1} + R_{2} = R

R_{1}^{2} + R_{2}^{2} = R^{2}

R_{1} + R_{2} < R

R_{1}^{2} + R_{2}^{2} < R_{2}

If the sum of the areas of two circles with radii $R_{1}$ and $R_{2}$ is equal to the area of a circle of radius R then

(a) $R_{1} + R_{2} = R$

(b) $R_{1} + R_{2} > R$

(d) $R_{1}^{2} + R_{2}^{2} = R^{2}$

r_{1}

r_{2}

r

r = r_{1} + r_{2}

{r_{1}}^{2} + {r_{2}}^{2} = r^{2}

r_{1} + r_{2} < r

{r_{1}}^{2} + {r_{2}}^{2} < r^{2}

R_{1} + R_{2} = R

R_{1} + R_{2} < R

R_{1}^{2} + R_{2}^{2} < R^{2}

R_{1}^{2} + R_{2}^{2} = R^{2}

Join BYJU'S Learning Program