Two parallel chords of a circle with diameter $13 c m$ are, $5 c m$ and $12 c m$ in length. If both the chords lies in a semi-circle, find the distance between the chords

8.5 c m

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5 c m

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3.5 c m

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3 c m

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Solution

The correct option is B $3.5 c m$
$O R = O S = O P = O Q = 6.5 c m$
From $Δ O A S$
$O A = \sqrt{O S^{2} - A S^{2}}$
$\to O A = \sqrt{(6.5)^{2} - (2.5)^{2}} = 6 c m$
From $Δ O B Q$
$O B = \sqrt{O Q^{2} - B Q^{2}}$
$\sqrt{(6.5)^{2} - 6^{2}} = 2.5$
$∴$ distance b/w chords is $O A - O B = 3.5 c m$

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Two parallel chords of a circle with diameter 13 cm are, 5 cm and 12 cm in length. If both the chords lies in a semi-circle, find the distance between the chords

The correct option is B 3.5 cmOR=OS=OP=OQ=6.5cmFrom ΔOASOA=√OS2−AS2→OA=√(6.5)2−(2.5)2=6cmFrom ΔOBQOB=√OQ2−BQ2√(6.5)2−62=2.5∴ distance b/w chords is OA−OB=3.5cm

Two parallel chords of a circle with diameter $13 c m$ are, $5 c m$ and $12 c m$ in length. If both the chords lies in a semi-circle, find the distance between the chords

The correct option is B $3.5 c m$
$O R = O S = O P = O Q = 6.5 c m$
From $Δ O A S$
$O A = \sqrt{O S^{2} - A S^{2}}$
$\to O A = \sqrt{(6.5)^{2} - (2.5)^{2}} = 6 c m$
From $Δ O B Q$
$O B = \sqrt{O Q^{2} - B Q^{2}}$
$\sqrt{(6.5)^{2} - 6^{2}} = 2.5$
$∴$ distance b/w chords is $O A - O B = 3.5 c m$