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A right $△ ABC$ right-angled at A is drawn to circumscribe a circle of radius 5 cm with center O. If AC = 17 cm and AB = 18 cm then OC is equal to

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10 cm

9 cm

13 cm

12 cm

answer is A.

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Detailed Solution

Given that a right

△ ABC

right-angled at A is drawn to circumscribe a circle of radius

5 cm

with center

O

. We have to find the length of OC.
By Pythagoras theorem, for a right-angle triangle ABC,

A C 2 = A B 2 + B C 2

, where AC is the hypotenuse of

△ A B C

.
Consider the figure,
Question Image

Here, OD is parallel to AB, corresponding angles are the same. So,

∠ A = ∠ D = 90 °

Therefore,

C D ⊥ O D

Given that, AC = 17cm . So,

A D + D C = 17 cm ⇒ 5 + DC = 17 ⇒ D C = 12 cm

By Pythagoras theorem, for a right-angled triangle ODC,

⇒ O C 2 = C D 2 + O D 2 ⇒ O C 2 = 122 + 52 ⇒ O C = 144 + 25 ⇒ O C = 169

Therefore, OC = 13cm.
Therefore, the correct option is 4.

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