Three distinct diameters are drawn on a unit circle such that chords are drawn as shown in the figure. If the length of one chord is \(\sqrt{2} \) units and the other two chords are of equal lengths, what is the common length of these chords?

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TopNewestsince radius is 1(unit circle). the angle opposite to the Root 2 side is 90 (converse of pythagoras theorem. hence its vertically opposite angle is also 90.

calling the centre as o and the diameter on which the 2 equal sides sit on as AB.one side as AC and the other equal side as BD since the radii are equal and AC=BD from sss postulate angle BOD = angle AOC Since they are on a straight line with one angle as 90 degrees angle AOC=angle bod=45

then use cosine rule to get the answer – Pranav Chakravarthy · 4 years, 4 months ago

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sqrt [ 2 - (sqrt 2) ] – Achint Gupta · 4 years, 4 months ago

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\(\sqrt (2- \sqrt 2)\) – Shourya Pandey · 4 years, 4 months ago

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root of 2-root 2

sorry didnt have time to put in latex – Pranav Chakravarthy · 4 years, 4 months ago

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– Ian Mana · 4 years, 4 months ago

nice can you explain how did you get it :DLog in to reply

– Lalit Shrinivas · 4 years, 4 months ago

easy thing ans- sqrt[2-sqrt(2)]Log in to reply

explain. – Tim Ye · 4 years, 4 months agoLog in to reply

\sqrt (2- \sqrt 2) – Anshul Agarwal · 4 years, 4 months ago

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We have a isosceles triangle whit a=x b=1 and angle at A is 45 (at B and C are 67.5 ) so we can make a right triangle witch has hypotenuse 1 and a side x/2. Since we have all the angles we can see that x/2 = 1

cos(67.5) so x=2cos(67.5) or x=2*sin(22.5) witch is approximately 0.765 – Djordje Marjanovic · 4 years, 4 months agoLog in to reply

I like this :] – Ksenia Solovieva · 4 years, 4 months ago

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Sweet.... – Rish Malviya · 4 years, 4 months ago

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sqrt(2-sqrt(2)). solved using basic geometry no trigonometry. – Andres Fabrega · 4 years, 4 months ago

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