09 – Rule 8

Alternate segment theorem 1:

Prove that the angle between the tangent and the chord (p) is equal to the angle in the alternate segment (q).


Hint: The line AC goes through the centre O so this is a straight line. Angle in a semi-circle?

Angle AOC is 180°,

angle ABC is angle in a semi-circle = 90°

Also the tangent at A is 90° to line AC

So BAC = 90° – p

Angle q must be equal to p

Hence p = q

Your Turn:

Find the value of P:

Enter your answer here:

Need some extra help? Find a tutor now

Or, call 020 3633 5145