Question

Two chords of lengths 16 cm and 17 cm are drawn perpendicular to each other in circle of radius 10 cm. The distance of their point of intersection from the centre is approximately

• A. 6.5 cm
• B. 7.2 cm
• C. 7.6 cm
• D. 8 cm

Answer 1

The correct option is D 8 cm

Let the two chords ABand CD of length 16 cm and 17 cm are drawn perpendicular to each other in a circle of radius 10 cm. Their point of intersection is P.
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$\therefore O{M}^2=O{A}^2-A{M}^2={10}^2-8^2=36$
$O{N}^2=O{C}^2-C{N}^2={10}^2-(8.5{)}^2$
$ON=\sqrt{100-72.25}=\sqrt{27.75}$
$\therefore$ Required distance
$=OP=\sqrt{O{M}^2+O{N}^2}$
$=\sqrt{36+27.75}$
$=\sqrt{63.75}\approx 8cm$