Question

30 points!

Which statement about BQ←→ is correct?
Please contact your teacher immediately if you do not see the image.

Question options:

BQ←→ is not a tangent line because ∠BAQ is an acute angle.

BQ←→ is not a tangent line because ∠BQA is an acute angle.

BQ ←→−is a tangent line because △ABQ is not a right triangle.

BQ←→ is a tangent line because m∠ABQ = 90° .

Answer 1

BQ←→ is not a tangent line because ∠BQA is an acute angle.

Explanation:

BQ←→ is not a tangent line because ∠BQA is an acute angle.BQ←→ is not a tangent line because ∠BQA is an acute angle.BQ←→ is not a tangent line because ∠BQA is an acute angle.BQ←→ is not a tangent line because ∠BQA is an acute angle.BQ←→ is not a tangent line because ∠BQA is an acute angle.BQ←→ is not a tangent line because ∠BQA is an acute angle.BQ←→ is not a tangent line because ∠BQA is an acute angle.BQ←→ is not a tangent line because ∠BQA is an acute angle.

Answer 2

Option (4) is correct about BQ

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°