Let ABC be an isoscles triangle with A B = A C.The bisector of ∠ B meets AC at D.Given that B C = B D + A D,we need to figure out ∠ A.

Question

Let ABC be an isoscles triangle with   A  B  =  A  C.The bisector of   ∠  B meets AC at D.Given that   B  C  =  B  D  +  A  D,we need to figure out   ∠  A.

Porter Mata · Accepted Answer

Step 1We take E on BC such that   B  E  =  B  D; so   E  C  =  B  C  −  B  E  =  B  C  −  B  D  =  A  D.Now we have a theorem that             A      B              B      C        =            A      D              D      C      ; so in   △  C  E  D and   △  C  A  B we have a common angle             C      E              C      D        =            A      D              C      D        =            A      B              C      B        =            C      A              C      B      .So we get   Δ  C  E  D     Δ  C  A  B so we have   ∠  C  D  E  =  ∠  D  C  E  =  ∠  A  B  C  =  2  x.Step 2Hence   ∠  B  D  E  =  ∠  B  E  D  =  4  x, so   9  x  =  180, or   x  =  20.Thus   ∠  A  =  180  −  4  x  =  100.

Let ABC be an isoscles triangle with AB=AC.The bisector of angle B meets AC at D. Given that BC=BD+AD, we need to figure out angle A.

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