Circle inscribed

There is a triangle ABC and a circle inscribed in this triangle with a radius of 15. Point T is the point of contact of the inscribed circle with the side BC. What is the area of the triangle ABC if | BT | = 25 a | TC | = 26?

Correct answer:

S =  1170

Step-by-step explanation:

r=15 BT=25 TC=26  BC=BT+TC=25+26=51  BS=r2+BT2=152+252=5 3429.1548 BZ=BS2r2=29.15482152=25  CS=r2+TC2=152+262=90130.0167 CY=CS2r2=30.01672152=26  AS2 = r2 + AZ2 AS2 = r2 + AX2  AX = AZ  sin β/2 = r : BS  β=π180°2 arcsin(r/BS)=π180°2 arcsin(15/29.1548)61.9275   sin γ/2 = r : CS  γ=π180°2 arcsin(r/CS)=π180°2 arcsin(15/30.0167)59.9633  α=180βγ=18061.927559.963358.1092   tan α/2 = r : AY  AY=r/tan(α/2)=15/tan(58.1092/2)=27 AZ=AY=27  AC=AY+CY=27+26=53 AB=AZ+BZ=27+25=52  s=(AC+AB+BC)/2=(53+52+51)/2=78  S=s (sAC) (sAB) (sBC)=78 (7853) (7852) (7851)=1170

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