A triangle ABC is drawn to circumscribing a circle of radius 3cm such that segments BD and DC into BC is divided by the point of contact D are of length 9cm. And 3 cm. Respectively. Find the sides AB and AC.
Asked by Amitej
14th December 2014,
4:33 PM
Answered by Expert
Answer:
Consider the above figure. We assume that the circle touches AB in F, BC in D and AC in E. Also given is BD = 9cm and DC = 3cm.Let AF = x.
For ΔABC, AF = AE = x (∵ tangents drawn from an external point to a circle are congruent i.e. AE and AF are tangent drawn from external point A.)
Similarly we have, BE = BD = 3cm (∵ congruent tangents from point B)
And CF = CD = 9cm (∵ congruent tangents from point C)
Now, AB = AE + EB = x + 3
BC = BD + DC = 12
AC = AF + FC = x + 9
Then,
2s = AB + BC +CA = x + 3 + 12 + 1 + x + 9 = 2x + 24
∴ s = x + 12
Using Heron’s formula,
Answered by Expert
15th December 2014,
5:40 PM
Rate this answer
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
You have rated this answer /10
Your answer has been posted successfully!
RELATED STUDY RESOURCES :
Browse free questions and answers by Chapters
Trending Tags
Latest Questions
JEE Main Mathematics
Asked by amaladelsingh
28th October 2020,
10:24 PM
CBSE X Biology
Asked by reenacharan2008
28th October 2020,
9:11 PM
