Tangent & Radius (Cambridge (CIE) IGCSE Maths)

• If you spot a tangent on a circle diagram, look to see if it meets a radius and label the right angle on the diagram

  • In some cases just doing this can earn you a mark!

• If you think you have spotted this circle theorem in a question, make sure it is a radius that meets the tangent, and not a chord

  • A radius passes through the centre of the circle

P and Q are points on the circle, centre O.

APB is a tangent to the circle at P.

(i) Explain why angle OPB is 90°.

(ii) Find the value of 

(i) 

Angle OPB is 90° because the angle between a tangent and a radius is 90° (and OP is a radius, and APB is a tangent).

(ii) As angle OPB is 90°, we can find angle OPQ 

OPQ = 90 - 53 = 37° 

As OP and OQ are both the radius of the circle, they have the same length. This means the triangle OPQ is isosceles, so the base angles (OPQ and OQP) are equal 

 Using the fact that the internal angles in a triangle sum to 180, we can find angle