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Find the circumferences of a circle inscribed in a rhombus with diagonals that are 12 cm and 16 cm long.

User Platalea Minor
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1 Answer

21 votes
21 votes

cmsee the figure below to better understand the problem

we have

AC=16 cm -------> OA=16/2=8 cm

BD=12 cm ------> OB=12/2=6 cm

Find out the value of x

Remember that

The area of the right triangle ABO is equal to

A=(1/2)(OB)(OA) ------> A=(1/2)(6)(8)=24 cm2

and the area of triangle ABO is equal to

A=(1/2)(AB)(x)

Find out the value of AB

Applying the Pythagorean Theorem

AB^2=OA^2+OB^2

AB^2=8^2+6^2

AB^2=100

AB=100

substitute

24=(1/2)(100)(x)

solve for x

24=50x

x=24/50

x=0.48 cm

The value of x is equal to the radius of the circle

so

the diameter is

D=2(0.48)

D=0.96 cm

Find the circumferences of a circle inscribed in a rhombus with diagonals that are-example-1
User Babak Abadkheir
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2.5k points