Question

AB=12cm and BC=16cm and AB perpendicular to BC , the radius of the circle passing through the points A,B,C is

Answer 1

<ABC=90
every angle inscribded in a semi circle is a right angle.
so, ABC is a semi circle.
thus AC is the diameter.
by applying pythagorus theorem,
AC^2=AB^2+BC^2
12^2+16^2
=144+256
=400
Sqrt OF 400=20
Diameter =20
radius=10 

Answer 2

Solution: -

Given: AB = 12 cm, BC = 16 cm and AB is ⊥ to BC

Method: 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