Question

Chord AB subtends two arcs with measures in the ratio of 1:5. Line l is tangent to a circle at point A. Find the measure of the angle between the tangent and secant AB
.

Answer 1

Answer:

the measure of the angle between the tangent and secant AB

= 150° or 30°

Step-by-step explanation:

Chord AB subtends two arcs with measures in the ratio of 1:5.

Line l is tangent to a circle at point A.

Let chord has angle x & 5x  

x + 5x = 360°

=> 6x = 360°

=> x = 60°

Then All angles of triangle formed by chord Ab with center

= 60°

Tangent angle with center = 90°

Measure of angle between Tangent and AB = 90° + 60°  or 90°-60°

= 150° or 30°