3

Part of 2020 LIMIT Category 1

Problems(2)

Source: LIMIT 2020

\overline{AC}

\overline{BD}

of a quaderilateral

ABCD

O

s_1

\triangle{AOB}

s_2

\triangle{OCD}

. Then show that

\sqrt{s_1}+\sqrt{s_2} \leq \sqrt{s}

Also find a geometrical condition for equality to hold (By geometrical condition we mean something like parallel lines, perpendicular lines,bisecting lines etc.)

Sum of Digit sum and digit product

Source: LIMIT 2020 Cat 1 Obj P3

2

n=ab

a

b

are digits) have the property that

n=a+b+a\times b

20

15

9

8