80.8k views
2 votes
Let AB be a chord of circle C(O,r) and suppose ℓ is the line tangent to C at B. Then the angle between AB and the line ℓ has measure ___________.

User Yoano
by
8.8k points

1 Answer

5 votes

Final answer:

The angle between the chord AB of a circle and the tangent line ℓ at B is 90 degrees because the radius is perpendicular to the tangent at the point of contact.

Step-by-step explanation:

The angle between the chord AB of circle C(O,r) and the tangent line ℓ at point B is 90 degrees. This occurs because the radius of a circle is perpendicular to the tangent at the point of tangency. By the definition of a tangent, it touches the circle at exactly one point and at that point, it forms a right angle with the radius drawn to the point of contact. The line AB, being a chord, includes the radius OB. As such, the angle formed between the chord AB and the tangent line ℓ at B, which includes the radius OB, is a right angle and thus measures 90 degrees.

User Andy Harvey
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories