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

1.	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» $\huge\bold\blue{QUESTION}$ 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✔️✔️✅ $\bold\purple{ADDITIONAL\: INFORMATION}$ 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)

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»

$\huge\bold\blue{QUESTION}$

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✔️✔️✅

$\bold\purple{ADDITIONAL\: INFORMATION}$

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)