The point a,b and c are on the circle such that ab is perpendicular to bc.ab =12cm, bc =16cm and ac is a diameter. find the radius of the circle passing through the point a,b and c
Answers
Given : AB = 12 cm, BC = 16 cm and AB is ⊥ to BC
Now, applying Pythagoras Theorem,
Hypotenuse² = Perpendicular² + Base²
⇒ AC² = AB² + BC²
⇒ AC² = 12² + 16²
⇒ AC² = 144 + 256
⇒ AC² = 400
⇒ AC = √400
AC = 20 cm
There is a relation between Hypotenuse (AC) and Circumradius (r).
The hypotenuse is the diameter of the circle and, and its center is exactly the midpoint of the hypotenuse.
So, Hypotenuse = 2r
Therefore,
r = hypotenuse/2
r = 20/2
Radius of the circle = 10 cm
If this is not clear, please refer another method in the
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ANSWER:
10cm
EXPLANATION:
Given:
AB = 12 cm,
BC = 16 cm
AB ⊥ BC
Method used : Pythagoras Theorem,
{ Hypotenuse² = Perpendicular² + Base²}
⇒ AC² = AB² + BC²
⇒ AC² = 12² + 16²
⇒ AC² = 144 + 256
⇒ AC² = 400
⇒ AC = √400
AC = 20 cm
Hypotenuse = AC = 2r
r = AC/2
r = 20/2
∴Radius = 10 cm