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?!

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Comments

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

A Former Brilliant Member - 8 years, 1 month ago

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

shaheed vh - 8 years, 1 month ago

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...

A Former Brilliant Member - 8 years, 1 month ago

@A Former Brilliant Member – Great Riya G . i appreciate you

shaheed vh - 8 years, 1 month ago

@Shaheed Vh – thankssss.....:)

A Former Brilliant Member - 8 years, 1 month ago

Math	Appears 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}`	$\boxed{123}$