MATH SOLVE

3 months ago

Q:
# Line AC is tangent to circle O at point CWhat is the measure of OAC?

Accepted Solution

A:

AC is a tangent so by definition, it touches the circle at exactly one point (point C) and forms a right angle at the tangency point. So angle ACO is 90 degrees

The remaining angle OAC must be 45 degrees because we need to have all three angles add to 180

45+45+90 = 90+90 = 180

Alternatively you can solve algebraically like so

(angle OAC) + (angle OCA) + (angle COA) = 180

(angle OAC) + (90 degrees) + (45 degrees) = 180

(angle OAC) + 90+45 = 180

(angle OAC) + 135 = 180

(angle OAC) + 135 - 135 = 180 - 135

angle OAC = 45 degrees

Side Note: Triangle OCA is an isosceles right triangle. It is of the template 45-45-90.Β

The remaining angle OAC must be 45 degrees because we need to have all three angles add to 180

45+45+90 = 90+90 = 180

Alternatively you can solve algebraically like so

(angle OAC) + (angle OCA) + (angle COA) = 180

(angle OAC) + (90 degrees) + (45 degrees) = 180

(angle OAC) + 90+45 = 180

(angle OAC) + 135 = 180

(angle OAC) + 135 - 135 = 180 - 135

angle OAC = 45 degrees

Side Note: Triangle OCA is an isosceles right triangle. It is of the template 45-45-90.Β