In the figure below, the rectangle at the corner measures 10 cm $\times$ 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?

10 cm

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40 cm

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50 cm

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None of these

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Solution

The correct option is C 50 cm

In the right angled $Δ$ , $r^{2} = (r - 20)^{2} + (r - 10)^{2}$
$= 2 r^{2} - 60 r + 500$
Solving, we get, r = 50

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In the figure below, the rectangle at the corner measures 10 cm × 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?

The correct option is C 50 cm In the right angled Δ, r2=(r−20)2+(r−10)2 =2r2−60r+500 Solving, we get, r = 50

In the figure below, the rectangle at the corner measures 10 cm $\times$ 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?

The correct option is C 50 cm

In the right angled $Δ$ , $r^{2} = (r - 20)^{2} + (r - 10)^{2}$
$= 2 r^{2} - 60 r + 500$
Solving, we get, r = 50