How to use congruence and angle bisector theorem for this geometry question involving isosceles triangle?Here is the diagram for the question:In triangle △ A D C , | A B | = | A C | = 8 and | N C | = 6. AN is the bisector of ∡ B A C . ∡ A D C = 2 ⋅ ∡ B C D . | D N | = x. Find x.

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How to use congruence and angle bisector theorem for this geometry question involving isosceles triangle?Here is the diagram for the question:In triangle   △      A    D    C  ,       |    A  B      |    =      |    A  C      |    =  8 and       |    N  C      |    =  6. AN is the bisector of   ∡      B    A    C  .   ∡      A    D    C    =  2  ⋅  ∡      B    C    D  .       |    D  N      |    =  x. Find x.

tkaljegs · Accepted Answer

Step 1Join BN. Note that   △  N  E  C  ≅  △  N  E  B and hence   ∠  N  B  C  =  α. So   ∠  B  N  D  =  ∠  N  B  C  +  ∠  N  C  B  =  2  α  =  ∠  N  D  B. So   △  B  N  D is isosceles with   B  D  =  B  N.Step 2Therefore,   B  D  =  B  N  =  C  N.            4      x      −      24        3    =  6Thus,   x  =  10.5.

In triangle ADC, |AB|=|AC|=8 and |NC|=6. AN is the bisector of ∡BAC. ∡ADC=2 * ∡BCD. |DN|=x. Find x.

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