Q. 15.0( 3 Votes )

A circle touches

Answer :


Given that a circle touches the sides BC, CA and AB of ΔABC at points D, E and F respectively.


Let BD = x, CE = y and AF = z.


We have to prove that area of ΔABC =


Proof:


BD and BF are tangents drawn from B. And D and F are points of contact.


BD = BF = x


Similarly for tangents CE and CD drawn by C and tangents AE and AF drawn from A,


CE = CD = y and AF = AE = z


Sides of ΔABC,


AB = c = AF + BF = z + x … (1)


BC = a = BD + DC = x + y … (2)


CA = b = CE + AE = y + z … (3)


In ΔABC, 2s = AB + BC + AC


= (z + x) + (x + y) + (y + z)


= 2 (x + y + z)


s = x + y + z … (4)


We know that area of ΔABC =


Area =


=


=


Hence proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Area Related to Circles- Important Formula and ConceptsArea Related to Circles- Important Formula and ConceptsArea Related to Circles- Important Formula and Concepts59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

ΔABC is an isosceGujarat Board Mathematics

P is in the exterGujarat Board Mathematics

P is the point inGujarat Board Mathematics

<img width="33" hGujarat Board Mathematics

In figure 11.24, Gujarat Board Mathematics

<img width="33" hGujarat Board Mathematics

Tangents from P, Gujarat Board Mathematics

The points of conGujarat Board Mathematics

A circle touches Gujarat Board Mathematics

<img width="33" hGujarat Board Mathematics