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#1 2020-04-05 06:06:37

Srikantan
Member
From: Tanjore
Registered: 2016-06-04
Posts: 42

Perimeter

In triangle ABC , AB = 3 ,BC=5 and CA = 6 . D and E are points on AC and BC respectively such that DE is a tangent to the Circle inscribed in triangle ABC. Find the perimeter of triangle CDE.

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#2 2020-04-05 19:25:13

Bob
Administrator
Registered: 2010-06-20
Posts: 8,914

Re: Perimeter

hi Srikantan

Have a look at this theorem:

http://www.mathisfunforum.com/viewtopic … 09#p365709

So you can write the perimeter in terms of the length of two tangents from C.

There's a formula for the radius given the sides of a triangle:

https://en.wikipedia.org/wiki/Incircle_ … gle#Radius

And cosine rule to get angle C and hence half C.  Then more trig to finish off.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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