Question

ABC is a right triangle such that AB = AC and the bisector of angle C intersects the side AB at D. Prove that AC+AD=BC

Answer 1

We have an equilateral right angle triangle,
Let AB=AC=1
the hypotenuse BC= sqrt(2) =r2

Applying the sine rule in the divided triangles gives
AD/1 =( 1-AD)/r2
Hence
AD (1+r2)=1
AD (1+r2)(r2-1)=r2-1
AD = r2-1
Or
r2 =1 +AD
BC=AC+AD

Hope it helps you

Answer 2

Answer:

Step-by-step explanation:

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mdafsarimam7867

Secondary SchoolMath 25+13 pts

ABC is a right triangle such that AB = AC and the bisector of angle C intersects the side AB at D. Prove that AC+AD=BC

Report by Nobita678 13.03.2018

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mdafsarimam7867

Mdafsarimam7867 · Virtuoso

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Løvé

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We have an equilateral right angle triangle,

Let AB=AC=1

the hypotenuse BC= sqrt(2) =r2

Applying the sine rule in the divided triangles gives

AD/1 =( 1-AD)/r2

Hence

AD (1+r2)=1

AD (1+r2)(r2-1)=r2-1

AD = r2-1

Or

r2 =1 +AD

BC=AC+AD

Hope it helps you