Question

Abc is a right triangle in which angle b=90.If ab=8 and bc=6cm, find the diameter of the circle

Answer 1

Answer:

Step-by-step explanation:

It's very easy

B= 90 °

Ab=8

Bc=6

So because of b is right angle

Form Right angle theorem

Ac is passes from center of circle it is diameter of circle

By Pythagoras theorem we find ac

(AC)² = 8²+6²

AC²= 64 +36

Ac²= 100

AC=√ 100

AC = 10

So diameter of circle is 10 cm

Answer 2

Let ABC be the right angled triangle such that ∠B = 90° , BC = 6 cm, AB = 8 cm. Let O be the centre and r be the radius of the in circle.

AB, BC and CA are tangents to the circle at P, N and M.

∴ OP = ON = OM = r (radius of the circle)

By Pythagoras theorem,

CA2 = AB2 + BC2

⇒ CA2 = 82 + 62

⇒ CA2 = 100

⇒ CA = 10 cm

Area of ∆ABC = Area ∆OAB + Area ∆OBC + Area ∆OCA

24 = 1/2r*AB + 1/2r*BC + 1/2r*CA

24 = 1/2r(AB+BC+CA)

r = 2*24 /(AB+BC+CA)

r = 48 /8+6+10

r = 48/24

r = 2

With Regards