Question

30 points!

Answer 1

Answer:

Option (4) is correct about BQ

Step-by-step explanation:

Given : From the figure : ∠BQA = 54° and ∠BAQ = 36°

Now, Since ∠BAQ = 36° > 30°  

So, ∠BAQ is not acute.

⇒ (1) is rejected.

Also, ∠BQA = 54° > 30°  

So, ∠BQA is not acute.

⇒ (2) is rejected.

Now, in ΔABQ, By using angle sum property of a triangle

∠BAQ + ∠BQA + ∠ABQ = 180°

⇒ 36° + 54° + ∠ABQ = 180°

⇒ ∠ABQ = 90°

Since, ∠ABQ is right angle so, (3) is rejected.

Now, ∠ABQ = 90° and the line which is exterior to the circle and makes right angle with the radius of the circle is always tangent to the circle.

Hence, Option (4) is correct about BQ.

Therefore, BQ is a tangent line because m∠ABQ = 90°