Math Is Fun Forum

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

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