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Question
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is ______.
Options
6 cm
8 cm
10 cm
12 cm
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Solution
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is 10 cm.
Explanation:
Given in the question, AB = 12 cm and BC = 16 cm.
In a circle, BC ⊥ AB. So, that means AC will be a diameter of circle.
Now, by using Pythagoras theorem in right-angled triangle ABC.
AC2 = AB2 + BC2
AC2 = (12)2 + (16)2
AC2 = 144 + 256
AC2 = 400
AC = 20 cm
So, radius of circle = `1/2 xx AC`
= `1/2 xx 20`
= 10 cm
Therefore, the radius of circle is 10 cm.
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