Answer :

Suppose that C is the largest circle, C_{1} is the circle with diameter 10 cm and C_{2} is the circle with diameter 24 cm aNd R, R_{1} and R_{2} are the radius of these circles respectively.

The diagram is given below:

Given: R_{1} = 5 cm [∵, Diameter = 10 cm]

R_{2} = 12 cm [∵, Diameter = 24 cm]

Area of circle C = Area of circle C_{1} + Area of circle C_{2}

⇒ πR^{2} = πR_{1}^{2} + πR_{2}^{2}

⇒ πR^{2} = π (R_{1}^{2} + R_{2}^{2})

⇒ R^{2} = (5)^{2} + (12)^{2}

⇒ R^{2} = 25 + 144 = 169

⇒ R = √169 = 13

If the radius of the largest circle is 13, then diameter is 2R.

Diameter = 2R

⇒ Diameter = 2(13) = 26

Hence, diameter of the largest circle is 26 cm.

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