Question

In a triangle abc , ab = ac. Points d and e are on the sides bc and ac respectively such that ad= ae. If angle bad =10°, then the measure of angle bad is

Answer 1

Thank you for asking this question. Here is your answer:

AD = AE (this is an equation 1)

AB = AC (this is an equation 2)

Now we will subtract AD from both sides, we will get this:

AB – AD = AC – AD  

AB – AD = AC - AE (Since, AD = AE)  

BD = EC (this is an equation 3)

Now we will divide equation 1 by 2.

AD/DB = AE/EC

We will use Thales’ theorem here  (DE‖BC )

∠DEC + ∠ECB = 1800

∠DEC + ∠CBD = 1800

So we know that quadrilateral BCED is cyclic.  

Therefore, B,C,E and D are the concylic points.

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