Waste less time on Facebook — follow Brilliant.
×

Find area of triangle

In triangle ABC with different rib inscribed circular with radius r=4 which touches AB at point M and M divided in two parts with length AM=8cm and MB=6cm.Find area of triangle ABC?!

Note by Arbër Avdullahu
4 years, 7 months ago

No vote yet
3 votes

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Is the answer 84 sq.units......

Riya Gupta - 4 years, 7 months ago

Log in to reply

Can you explain ? I think we should use property of tangents and incircle - perimeter of triangle relation

Shaheed Vh - 4 years, 7 months ago

Log in to reply

SORRY i got late

I used the same...... we can consider 'r' be the radii of incircle and we know (according to solutions of triangle) that
r=(area of triangle/semiperimeter of triangle) ,,which can be furthr written as

   r =  \sqrt{\frac{(s-a)(s-b)(s-c)}{s}}.

lets consider the circle touches triangle at pts M,N,P on sides AB,AC,BC respctivly since when we draw tangents from a point on circle they r equal in length thrfore AM=AN=8 MB=BP=6 PC=CN= x

NOW USING THIS FORMULA

r = \sqrt{\frac{(s-a)(s-b)(s-c)}{s}}

where r is radii=4

s = \frac{a+b+c}{2}

a,b,c are sides opp. to A,B,C resp. i.e. a=6+x ; b=8+x ; c=8+6=14

we can find x
and use 
r= \frac{area of triangle}{s}

an finally the answer i got is 84...

Riya Gupta - 4 years, 7 months ago

Log in to reply

@Riya Gupta Great Riya G . i appreciate you

Shaheed Vh - 4 years, 7 months ago

Log in to reply

@Shaheed Vh thankssss.....:)

Riya Gupta - 4 years, 7 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...