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Chord of Contact: Ellipse

OC and OD a...

Question

$¯ ¯¯¯¯¯¯ ¯ O C$ and $¯ ¯¯¯¯¯¯¯ ¯ O D$ are distinct radii of $⨀ (0, r)$ and $¯ ¯¯¯¯¯¯ ¯ O C ⊥ ¯ ¯¯¯¯¯¯¯ ¯ O D$ . Tangents drawn from $C$ and $D$ intersect each other in $A$ . If $O A = 5 \sqrt{2}$ then find $r$ .

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Solution

In $Δ A O D$
$cos 45^{\circ} = \frac{r}{5 \sqrt{2}}$
$\frac{1}{\sqrt{2}} = \frac{r}{5 \sqrt{2}}$
$r = 5 u n i t$

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