Question

e
A rligt triangle ABC
right angle at
А as drawn to Scurmscribe
circle of radius
5cm
with
o if AC=17cm
and AB = 18c
m then find length
of oc.
کا

​

Answer 1

Answer:

The value of OCOC is 13\ cm13 cm

Step-by-step explanation:

Given,

\triangle ABC△ABC is the right triangle and \angle A∠A is right angle, Circumscribe a circle of radius 5\ cm5 cm with center OO and AC=17\ cm,AB=18\ cmAC=17 cm,AB=18 cm

In figure,

OD\parallel ABOD∥AB and ADOEADOE become a square.

So, AD=5\ cmAD=5 cm (∵ OD=5\ cmOD=5 cm )

DC=AC-ADDC=AC−AD

⇒DC=17-5DC=17−5

⇒DC=12\ cmDC=12 cm

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

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

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

2=OD

2 +DC

2

⇒OC=\sqrt{12^{2}+5^{2}}OC=

12

2+5

2

⇒OC=\sqrt{144+25}OC=

144+25

∴OC=13OC=13

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