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

If $AB = 12$ cm, $BC = 16$ cm and $AB$ is perpendicular to $BC$ , then which of the following is the radius of the circle passing through the points $A$ , $B$ and $C$ ?

A
$6 cm$
B
$8 cm$
C
$10 cm$
D
$12 cm$

Solution:

Given-

A, B

C

are points such that

AB = 12 cm

and

BC = 16 cm

BC ⊥ AB

.
Constructing the figure according to the given data,

i.e.

∠ ABC = 90^{0}

Then,

ΔABC

is a right triangle with

AC

as hypotenuse.
By Pythagoras theorem,

{AC}^{2} = {AB}^{2} + {BC}^{2}

{AC}^{2} = {(12}^{2} + 16^{2})

{AC}^{2} = (144 + 256)

{AC}^{2} = 400 {cm}^{2}

AC = 20 cm

Here, the circle passing through

A, B

C

will have its diameter as

AC

∴ Radius = \frac{Diameter}{2}

r = \frac{AC}{2}

r = \frac{20 cm}{2}

r = 10 cm

Hence, the radius is

10 cm

.
Therefore, option 3 is correct.

If $AB = 12$ cm, $BC = 16$ cm and $AB$ is perpendicular to $BC$ , then which of the following is the radius of the circle passing through the points $A$ , $B$ and $C$ ?

Solution:

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