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The length of chord of a circle is $22\,\text{cm}$ and the perpendicular distance between the centre and the chord is $60\,\text{cm}$ . Find the radius of the circle.

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Pythagorean theorem

Full solution

Q. The length of chord of a circle is

22\,\text{cm}

and the perpendicular distance between the centre and the chord is

60\,\text{cm}

. Find the radius of the circle.

Draw Shapes: Draw the circle, chord, and perpendicular line from the center to the chord. This forms two right-angled triangles.
Chord Bisects: The perpendicular line bisects the chord, so each half of the chord is $11\,\text{cm}$ ( $22\,\text{cm} / 2$ ).
Pythagorean Theorem: Use the Pythagorean theorem to find the radius $r$ . The perpendicular distance $60\,\text{cm}$ and half the chord $11\,\text{cm}$ are the two legs of the right triangle, and the radius is the hypotenuse.
Write Equation: Write down the Pythagorean theorem: $a^2 + b^2 = c^2$ , where $a$ is $60\,\text{cm}$ , $b$ is $11\,\text{cm}$ , and $c$ is the radius $(r)$ .
Calculate Squares: Plug in the values: $60^2 + 11^2 = r^2$ .
Add Squares: Calculate the squares: $3600 + 121 = r^2$ .
Take Square Root: Add the squares: $3600 + 121 = 3721$ .
Calculate Radius: Take the square root of both sides to solve for $r$ : $\sqrt{3721} = r$ .
Calculate Radius: Take the square root of both sides to solve for $r$ : $\sqrt{3721} = r$ .Calculate the square root: $r = 61$ .

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