AP EAMCET Engineering 22 Sep 2020 Shift 2 Paper

Let P,Q,R and S are the mid-point of sides of a quadrilateral ABCD respectively.
P= mid-point of AB=‌

a+b

2

Q= mid-point of BC=‌

b+c

2

R= mid-point of CD=‌

c+d

2

S= mid-point of AD=‌

a+d

2

Mid-point of PR=‌

‌ a+b 2 + c+d 2

2

=‌

a+b+c+d

4

Mid-point of SQ=‌

‌ a+b 2 + c+d 2

2

=‌

a+b+c+d

4

∴E= mid-point of PR= mid-point of SQ
∴‌‌OE=‌

a+b+c+d

4

4OE=a+b+c+d
∴OA+OB+OC+OD=4OE
xOE=4OE
x=4