Ask & Answer: India's Largest Education Community

If two circles intersect at two distinct points

->|r₁ – r₂| < C₁C₂ < r₁ + r₂

| r – 2| <  $\sqrt[]{9+16}$ < r + 2

|r – 2| < 5                     and r + 2 > 5

–5 < r 2 < 5                    r > 3                      … (2)

–3 < r < 7                                                        (1)

From (1) and (2)

3 < r < 7

Area of ?

$=\frac{1}{2}\left|\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ \hfill x\hfill & \hfill y\hfill & \hfill 1\hfill \\ \hfill -x\hfill & \hfill y\hfill & \hfill 1\hfill \end{array}\right|$

-> $\left|\frac{1}{2}\left(xy+xy\right)\right|=\left|xy\right|$

->Area (D) = |xy| = |x (– 2x² + 54x)|

$\frac{d\left(\Delta \right)}{dx}=\left|\left(-6x^2+108x\right)\right|\Rightarrow \frac{d\Delta }{dx}=0$  at x = 0 and 18

->at x = 0, minima

and at x = 18 maxima

Area (D) = |18 (– 2 (18)² + 54 × 18)| = 5832

The authority activated the UPSC IES 2026 application apply link on the official website at upsconline.nic.in. Candidates can apply via direct link provided on this page as well.

Yes. Exeter University accepts students from countries across the globe. There are more than 7,800 international students currently on the campus grounds, of which 800+ account for Indian-origin.

Michigan State has been consistently ranked by ARWU Shanghai ranking body over the years. In the past 3 years, its MSU's ARWU ranking has witnessed a dropping trend. In the 2024 ranking, the university was ranked at #136 globally, however, this ranking dropped to #161 in 2026. 

It also ranked university's courses in the field of Law (#28), Sociology (#76) and Political Science (#51) in 2024.