Question

A circle of diameter 13 cm has two chords of length 12 cm and 5 cm. If both the chords lie in the same semi-circle, what is the distance between the chords?

• A. 8.5 cm
• B. 5 cm
• C. 3.5 cm
• D. 3 cm

Answer 1

The correct option is C

3.5 cm

Here, $r=\frac{13}{2}cm=6.5cm$
$OP=\sqrt{{\left(\frac{13}{2}\right)}^2-{\left(\frac{12}{2}\right)}^2}=\sqrt{\frac{169}{4}-\frac{144}{4}}$ [Perpendicular from the centre bisects the chord]
$=\frac{5}{2}cm$
$OQ=\sqrt{{\left(\frac{13}{2}\right)}^2-{\left(\frac{5}{2}\right)}^2}=\sqrt{\frac{169}{4}-\frac{25}{4}}$
$=\frac{12}{2}=6cm$
$\therefore PQ=OQ-OP=6-\frac{5}{2}=\frac{7}{2}=3.5cm$