Question

एक त्रिभुज ABC में, समकोण B पर है, BC = 15 सेंटीमीटर और AB=8 सेंटीमीटर है। यदी त्रिभुज ABC का परिवृत्त बनाया गया है, तो वृत्त की त्रिज्या ज्ञात कीजिए । A)4cm B)3cm C)1cm D)2cm​

Answer 1

Step-by-step explanation:

In right angled triangle ABC , AC^2 = AB^2+BC^2.

or. AC^2 = 8^2+15^2 =289. or. AC= 17 cm.

Area of triangle ABC= (8×15)/2 = 60 cm^2.

s = (AB+BC+CA)/2.=(8+15+17)/2= 20 cm.

Radius (r) of inscribed circle = area of ∆/s = 60 cm^2/20 cm. = 3 cm. Answer.

Given :

ABC is a right angled triangle.

Angle, B = 90°

AB= 8cm

BC=15 cm.

Let the ra8dius of the incircle be, r.

r=A/s

Where A=area of the triangle.

s= semi perimeter

A=15x8/2 =60 cm.

s= (AB+ BC + CA)/2

Here AB, BC are given. CA is to be found out.

CA= √(AB^2+BC^2)= √(8^2+15^2)

√(64+225)=17

Therefore, s= ( 8+15+17)/2=20

r = A/s = 60/20=3 cm.