If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm then what is t...........

Quantitative Aptitude (CDS) Coordinate Geometry

If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two chords?

1 cm or 7 cm

2 cm or 14 cm

3 cm or 21 cm

4 cm or 28 cm

Case – 1

When both the chords are in two different halves of the circle
Distance between chords = OM + ON = $\sqrt{r^{2}- ND^{2}} + \sqrt{r^{2}- NB^{2}}$

$=\sqrt{10^{2}- (\frac{12}{2})^{2}} + \sqrt{10^{2}- (\frac{16}{2})^{2}} =8\: cm +6 \: cm = 14\: cm$

Case - 2

When both the chords are in two different halves of the circle

$Distance\: between\: two\: chords\: = OM+ ON= \sqrt{r^{2}- ND^{2}} + \sqrt{r^{2}- MB^{2}}$

$=\sqrt{10^{2}- (\frac{12}{2})^{2}} + \sqrt{10^{2}- (\frac{16}{2})^{2}}$

= 8 cm - 6cm = 2 cm

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