Question

OABC is a rhombus, three of
whose vertices lie on a circle with centre O.
If the area of the rhombus is 18√3 cm^2, find
the perimeter and area of the circle
(take π= 3.14].​

Answer 1

Answer:

Step-by-step explanation:

O is centre of the circle

OPQR is a rhombus.

Let the diagonals OQ and PR intersect at S

area of rhombus OPQR = 32√3 cm2

Let

OP = OQ = OR = r

OS = SQ = r/2

RS = PS

In right ΔOSP

By Pythagoras theorem

OP² = OS² + PS² 

r² = (r/2)² + PS²

PS² = r² – (r/2)² 

= 3r²/4

so, PS = (√3r/2)

 PR = 2PS = √3r

area of rhombus = 1/2 x d₁ x d₂

area of rhombus OPQR = 1/2 x OQ x PR

32√3 = 1/2 x r x √3r

32 = 1/2 r²

r² = 64

r = 8

Area of circle = πr² 

= 22/7 x 8²

= 201. 14 sq cm 

Answer 2

Answer:

37.68cm and113. 04cm

Step-by-step explanation:

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