Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length If...........

Quantitative Aptitude (CDS) Coordinate Geometry

Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then the distance between these chords is

5.5 cm

5 cm

3.5 cm

3 cm

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Explanation:

In $\Delta$ OAB
$OA=\sqrt{(\frac{13}{2})^{2}-(6)^{2}}$
$OA=\sqrt{(\frac{13}{2})^{2}-(6)^{2}} = \sqrt{\frac{25}{4}}=5/2=2.5\: cm$
In $\Delta$ ODC
$OD=\sqrt{(\frac{13}{2})^{2}-(\frac{5}{2})^{2}} = \sqrt{\frac{144}{4}}=12/2=6\: cm$
Distance between two chords = OD - OA = 6 - 2.5 = 3.5 cm