Question

. A right triangle ABC right angled A drawn to circumscribe a circle of radius 5 cm with centre O. IAC = 17
and AB = 18 cm, then OC =
(a) 10 cm
(b) 9 cm
(c) 12 cm
(d) 13 cm​

Answer 1

Step-by-step explanation:

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Answer 2

The value of $OC$ is $13\ cm$

Step-by-step explanation:

Given,

$\triangle ABC$ is the right triangle and $\angle A$ is right angle, Circumscribe a circle of radius $5\ cm$ with center $O$ and $AC=17\ cm,AB=18\ cm$

In figure,

$OD\parallel AB$ and $ADOE$ become a square.

So, $AD=5\ cm$ (∵ $OD=5\ cm$ )

$DC=AC-AD$

⇒$DC=17-5$

⇒$DC=12\ cm$

$\angle ODC=90\ degree$ (∵ $OD\parallel AB$ and corresponding angle are equal)

From $\triangle OCD$ also right-angle triangle,

$OC^{2}=OD^{2}+DC^{2}$

⇒$OC=\sqrt{12^{2}+5^{2}}$

⇒$OC=\sqrt{144+25}$

∴$OC=13$

So, The value of $OC$ is $13\ cm$