Here's the question bank on all the general aptitude topics.
Given a semicircle with O as the centre, as shown in the figure, the ratio \(\frac{{\overline {AC} + \overline {CB} }}{{\overline {AB} }}\) is _____, where \(\overline {AC} ,\;\overline {CB} \;\;and\;\;\overline {AB} \) are chords.
Let the radius of the semicircle is r as shown in the diagram given below.Now, OA = OC = OB = rAB = OA + OB = 2r\(\overline {AC} = \sqrt {{{\left( {OA} \right)}^2} + {{\left( {OC} \right)}^2}} = \sqrt {{r^2} + {r^2}} = \sqrt 2 r\)\(\overline {BC} = \sqrt {{{\left( {OB} \right)}^2} + {{\left( {OC} \right)}^2}} = \sqrt {{r^2} + {r^2}} = \sqrt 2 r\)The ratio \(\frac{{\overline {AC} + \overline {CB} }}{{\overline {AB} }} = \frac{{\sqrt 2 r + \sqrt 2 r}}{{2r}} = \sqrt 2 \)
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