Question

Find the angles marked with letters. Give reasons for your answers. O is the centre of the circle. C 80% >B​

Answer 1

Answer:

f = 50 degrees
g = 40 degrees

Step-by-step explanation:

Triangle ABC is isosceles as AB = AC as they are both tangents that exit from the same external point to the same circle.

Therefore, <A = <C = f.

The sum of all angles in a triangle is 180 degrees, therefore:

$80 + f + f = 180\\2f = 100\\f = 50 \text{ degrees}$

<OAB is a right angle as a tangent line to a circle is perpendicular to the radius of that circle in the point of intersection.

<OAB is made of <OAC = g and <CAB (= f = 50 degrees), therefore <OAC (= g) is simply the difference between <OAB and <CAB:

$< \text{OAC} = < \text{OAB}- < \text{CAB}\\\to g = 90 - f\\\to g = 90 - 50 = 40 \text{ degrees}$