A geometry problem by Syed Hissaan

Geometry Level 2

Given that form the figure A B = 2 x AB=2x , assume a point O O is on the circumference on semicircle such that O B = x OB=x and O A = 1 OA=1 , then find the value of x x .

Give your answer up to 2 decimal places.


The answer is 0.58.

Syed Hissaan by Syed Hissaan , 20, Pakistan

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2 solutions

Angle AOB is 90. Using Pythagorean, OA^2+OB^2=AB^2=>1^2+x^2=(2x)^2=>x=1/sqrt3

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Syed Hissaan
Sep 2, 2016

simply join the point P to A and B This will create a right angle triangle (bcoz angle in a semi circle is a right angle i.e 90 degrees ) now using the pythagoras theorem , AP ^1/2 = AB ^1/2 + PB ^1/2 solving this yields AP= 1 3 1 / 2 \frac{1}{3^1/2} calculating this gives 0.577 => 0.58 ;

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