Question

ln the figure the line PQ is a tangent to the circle. If angle PAC=65 degree and angle QAB=50 degree. find the measure of the following angles. angle BAC,angle ACB,angle D​

Answer 1

Answer:

BAQ=30

∘

Since AB is the bisector of ∠CAQ

∠CAB=∠BAQ=30

∘

∠CAQ=∠CAB+∠BAQ=60

∘

We can also see that: ∠PAC+∠CAQ=180

∘

So,∠PAC=120

∘

Since AD bisects ∠PAC

So,∠PAD=∠DAC=

2

∠PAC

=60

∘

So,∠DAB=90

∘

And we know that only diameter subtends an angle of 90

∘

on the circle

Hence part (I) is proved

Now we see that ∠CAB & ∠ACBare equal because they share a same side in front on them

Finally we can see two angles same in ΔABCSo it is an Isosceles triangle, Hence (II) is proved

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