A 5 by 12 rectangle is inscribed in a circle. What is the circumferenc

Explanation:

r^2 = 6^2 + (5/2)^2
r^2 = 36 + 25/4
r^2 = (144+25)/4
r = 13/2
r = 6.5

Circumference of cirle = 2πr = 2x6.5xπ = 13π

IMO-B

rectangle would give a right angled ∆ 5:12:13
so radius of circle is 6.5
and circumference 13pi
option B

Using Pythagoras theorem, sq(5) + sq(12) = \sqrt{169} = 13
Diameter= 13
Radius = 13/2

Hence, circumference is 2*pi*r (\(13\pi\))
IMO B

When a rectangle is inscribed in a circle, the Diagonal of the rectangle = Diameter of the circle

Diagonal of the rectangle = sqrt (5^2 + 12^2 ) = 13 = 2*RADIUS

Circumference = pi * 2 * radius = 13 * pi

IMO B

A 5 by 12 rectangle is inscribed in a circle. What is the circumference of the circle?

Given:
Rectangle Length and Width
Rectangle inscribed in a circle

Need:
Circumference of circle

We know that Circumference C = 2πr
We need either diameter or radius to find the circumference.

The two sides of a rectangle gives us a right triangle. So we have 2 sides of triangle as 5 & 12. Now based on triangle triplets we know that this is a 5-12-12 triangle without using any calculation. So the third side i.e hypotenuse is 13.

We also know that third side hypotenuse of rectangle is equal to diameter of circle.

So D = 13 or 2r=13
Circumference = 2πr = 13π

Ans: B
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A 5 by 12 rectangle is inscribed in a circle. What is the circumference of the circle?

Diagonal of the rectangle = Diameter of the circle = d

Clearly, it is a 5-12-13 triangle.
so, d=13

Circumference = πd
=13π

Option B

Solution:

If a rectangle is inscribed in a circle, its diagonal is the diameter of the circle. Since the rectangle has dimensions of 5 and 12, its diagonal must be 13 since the two dimensions of the rectangle and the diagonal form a 5-12-13 right triangle. Therefore, the diameter of the circle is 13, and its circumference is 13π.

Answer: B
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