Question

Find the length of radius.

Answer 1

radius = 7.5 cm

Explanation:

OM is the perpendicular bisector of AB, thus

∠ OMB = 90° and MB = 6 cm with OB being the radius of the circle

Using Pythagoras' identity in right triangle OMB

OB² = MB² + OM² = 6² + 4.5² = 36 + 20.25 = 56.25 ( square root both sides )

OB =
`√(56.25)` = 7.5

The radius = OB = 7.5 cm

Answer 2

`\boxed{r = 7.5\ cm}`

Explanation:

If M is the midpoint so AM = BM = AB/2 = 12 / 2 = 6 cm

Let's Consider a ΔOMB which would be a right angled triangle. So, We can use Pythagorean theorem to find the radius of the circle:

`c^2 = a^2+b^2`

Where c is hypotenuse (radius) , a is base ( MB = 6 cm ) , b is the perpendicular (OM = 4.5 cm)

`r^2 = 6^2+4.5^2\\r^2 = 36+20.25\\r^2 = 56.25`

Taking sqrt on both sides

r ≈ 7.5 cm