Question

A circle of diameter 13 cm has two chords of lenght 12cm and 5cm. If both the chords lie on the same semicircle, 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, $r=\frac{13}{2}cm=6.5cm$
$OP=\sqrt{{\left(\frac{13}{2}\right)}^2-{\left(\frac{12}{2}\right)}^2}=\sqrt{\frac{169}{4}-\frac{144}{4}}$
$=\frac{5}{2}cm$
$OQ=\sqrt{{\left(\frac{13}{2}\right)}^2-{\left(\frac{5}{2}\right)}^2}=\sqrt{\frac{169}{4}-\frac{25}{4}}$
$=\frac{12}{2}=6cm$
$\therefore PQ=OQ-OP=6-\frac{5}{2}=\frac{7}{2}=3.5cm$