# The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.

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The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.

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Area of Circle = Area of circle with radius 8 cm + Area of circle with radius 6 cm

πr2 = π(8)2 + π(6)2

πr2 = 64π + 36 π

r2 = 100

or r = 10

Radius of the circle is 10 cm.

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Let the radius of the first circle be r1
and second circle be r2.
third circle be R.
Given,
r1=8cm.r2=6cm.
A/q.
phi R^2=phi r1^2+phi r2^2.
phi R^2=phi(8^2+6^2).
R^2=64+36
R^2=100
R=10.
therefore the radius of the third circle of 10.CM.

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