In a circle, $A B$ and $C D$ are two parallel chords with centre $O$ and radius $10 c m$ such that $A B = 16 c m$ and $C D = 12 c m$ determine the distance between the two chords?

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Solution

Length of the chord $(A B) = 16 c m$
$\begin{matrix} ∴ A F = \frac{1}{2} \times 16 = 8 c m \end{matrix}$
Length of the chord $(C D) = 12 c m$
$∴ C E = \frac{1}{2} \times 12$
$= 6 c m$
In the right $△ O C E$ ,
$\begin{matrix} O E^{2} = O C^{2} - C E^{2} = 10^{2} - 6^{2} = 100 - 36 = 64 O E = \sqrt{64} = 8 c m In the right Δ O A F O F^{2} = O A^{2} - A F^{2} = 10^{2} - 8^{2} = 100 - 64 = 36 O E = \sqrt{36} = 6 c m \end{matrix}$
Distance between the two chords
$\begin{matrix} = O E + O F = 8 + 6 = 14 c m \end{matrix}$

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In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB=16 cm and CD=12 cm determine the distance between the two chords?

Length of the chord (AB)=16 cm ∴AF=12×16=8 cm Length of the chord (CD)=12 cm ∴CE=12×12 =6 cm In the right △OCE, OE2=OC2−CE2=102−62=100−36=64OE=√64=8 cm In the right ΔOAFOF2=OA2−AF2=102−82=100−64=36OE=√36=6 cm Distance between the two chords =OE+OF=8+6=14 cm

In a circle, $A B$ and $C D$ are two parallel chords with centre $O$ and radius $10 c m$ such that $A B = 16 c m$ and $C D = 12 c m$ determine the distance between the two chords?