Question

A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
A) 2.5π B) 3π C) 5π D) 4π

Answer 1

$\huge\bold\blue{QUESTION}$

A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A) 2.5π B) 3π C) 5π D) 4π

$\huge\bold\red{ANSWER}$

Let ABCD be a rectangle inscribed in circle with centre O

As, we know that, The point of meet of diagonals passes through centre of circle.

So, BD and AC of diagonals

The diagonals of rectangle bisect each other

So,AO=OC=AC/2 = radius of circle

DIAGONAL OF RECTANGLE=

$= \sqrt{ {l}^{2} + {b}^{2} }$

$= \sqrt{ {3}^{2} + {4}^{2} } \\ \\ = \sqrt[2]{9 + 16} \\ \\ = \sqrt{25} \\ \\ = 5cm$

NOW THE RADIUS OF CIRCLE WE GOT=5/2CM

CIRCUMFERENCE OF CIRCLE=2πr

=2×π×5/2

=5π

SO OPTION C) 5π✔️✔️✅

$\bold\</strong><strong>p</strong><strong>u</strong><strong>r</strong><strong>p</strong><strong>l</strong><strong>e</strong><strong>{</strong><strong>ADDITIONAL\</strong><strong>:</strong><strong> INFORMATION</strong><strong>}$

1)A rectangle is inscribed in a circle whose equation is x²+ y² = r² or

$y=\sqrt{{r}^{2}-{x}^{2}}$

where r is the radius of the circle. The diameter d of the circle is the diagonal AC OR BD of the rectangle.

2)AREA OF A CIRCLE=πr²

3)CIRCUMFERENCE=2πr

4)AREA OF SQUARE=a². (a = side of square)

5) Perimeter of Square=4a. (a=side of square)

6)AREA OF rectangle=l×b. (l= length, b=

breadth)

7)Perimeter of rectangle=2(l+b)

Answer 2

Refer to the above ans

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