A circle with centre p is inscribed in the ∆ABC. Side AB,side BC and side AC touch the circle at points L,M and N respectively. Radius of the circle is r
Prove that :
A(∆ABC)=1:2(AB+BC+AC)×r
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Answer:
Step-by-step explanation:
Consider is the center of the circle.
Radius of the circle =
Prove that
Draw lines between and
AB is tangent on the circle, touch the circle at the point L, and PL is the radius.
According to the tangent radius theory
therefore we can proved that
We know that,
And
Therefore,
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