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

$(x - 20)^{2} + (x - 10)^{2} = x^{2}$
$x^{2} + 400 - 40 x + x^{2} + 100 - 20 x = x^{2}$
$x^{2} - 60 x + 500 = 0$
$x^{2} - 50 x - 10 x + 500 = 0$
$x (x - 50) - 10 (x - 50) = 0$
$x = 50, x = 10.$
$Q x c a n n o t b e 10.$
$∴ x = 50.$

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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 (x–20)2+(x–10)2=x2 x2+400–40x+x2+100–20x=x2 x2–60x+500=0 x2–50x–10x+500=0 x(x–50)–10(x–50)=0 x=50,x=10. Q x cannot be 10. ∴x=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

$(x - 20)^{2} + (x - 10)^{2} = x^{2}$
$x^{2} + 400 - 40 x + x^{2} + 100 - 20 x = x^{2}$
$x^{2} - 60 x + 500 = 0$
$x^{2} - 50 x - 10 x + 500 = 0$
$x (x - 50) - 10 (x - 50) = 0$
$x = 50, x = 10.$
$Q x c a n n o t b e 10.$
$∴ x = 50.$