# Geometry

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Two parallel chords of lenght 24cm and 10cm which lie on opposite side of a circle are 17cm apart. Calculate the radius of the circle to the nearest whole number.

• Geometry -

it's difficult to explain it here because you need to draw to see it clearly. i'll provide a link to for you to see the drawing (though it's little unclear :P)

first you draw the circle and the parallel chords. connect the center of circle to one of the endpoints of the two chords. represent connect the the center of circle and the center of the chords. you will for two right triangles.
let x = the base of one of the right triangles formed, and
let 17-x = the base of the other right triangle.
do Pythagorean theorem for both. equate the r^2. the x^2 will cancel each other and you'll be able to solve for x.
x = 5 and
17 - x = 12
now you substitute this back to either equation.
r^2 = 144 + x^2
r^2 = 144 + 5^2
r^2 = 144 + 25 = 169
r = 13 cm

here's the link. i drew this on sticky notes using tablet and it's a little unclear lol: h t t p : / / i 4 1 . t i n y p i c . c o m / z x t p 9 0 . p n g

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Diagram

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