Question

3.
ABC is a right angled triangle, right angled at B such that BC = 6 cm and AB = 8 cm. A circle with centre o is
inscribed in 1ABC. The radius of the circle is
B
2 cm
(C) 3 cm
(D) 4 cm​

Answer 1

Radius of the circle is 2 cm.

Since ABC is a Right Angled Triangle, using Pythagorus Theorem:

$AB^2 + BC^2 = AC^2\\\\Therefore, 8^2 + 6^2 = AC^2\\AC = 10$

Now lets take the Radius of circle = r

And the points the circle, touches the triangle be:

D on AB, E on BC and F on AC

Now, using Circles theorem, OD, OE and OF all the perpendiculars as, AB, BC and AC are tangents to the circle.

In figure DOEB,

BD = BE

And, OD = OE

And, Angle D = B = E = 90

So Angle O = 360 - 270 = 90

Using these facts we can say figure DOEB is a square.

So r = BD = BE

Now, using Tangents theorem,

AD = AF, BD = BE, CE = CF

Using this we can say,

AD = AF = 8-r

CE = CF = 6-r

8-r + 6-r = 10

Therefore, r = 2