Question

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 ___________.

Answer 1

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.