Key to "Draw any circle O and any circle P...."

Maiclubk

Answered question

2021-08-08

Draw any circle O and any circle P. Construct a circle whose area equals the sum of the areas of circle O and circle P.

firmablogF

Skilled2021-08-09Added 92 answers

Given:
There are three different type of circles given.
Area of a circle:
Consider a circle with centre o and radius r,
area of the circle is

π r^{2}

Answer:
Let O be any circle with radius

r_{1}

Area of the circle is

π r_{1}^{2}

Let P be any circle with radius

r_{2}

Area of the circle is

π r_{2}^{2}

sum of the area of the circle O and P is

π r_{1}^{2} + π r_{2}^{2} = π (r_{1}^{2} + r_{2}^{2}) \to (1)

Let Q be the circle with radius

\sqrt{(r_{1}^{2} + r_{2}^{2})}

Area of the circle Q is

π (r_{1}^{2} + r_{2}^{2}) \to (2)

from (1) and (2), we get the sum of the area of the circle O and P is equal to the area of the circle Q.

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