Angle Properties of Circles

O is the centre and PT is a tangent to the circle at T.

Find the value of x.

O is the centre and PT is a tangent to the circle at T.

Find the values of x and y.

• x = 45⁰, y = 90⁰

• x = 45⁰, y = 45⁰

• x = 90⁰, y = 45⁰

• x = 90⁰, y = 90⁰

O is the centre and PT is a tangent to the circle at T.

Find the value of b.

O is the centre and PT is a tangent to the circle at T.

Find the values of a and b.

• a = 35⁰, b = 110⁰

• a = 55⁰, b = 70⁰

• a = 72.5⁰, b = 35⁰

• a = 35⁰, b = 55⁰

O is the centre and PT is a tangent to the circle at T.

Find the values of p, q and r.

• p = 25⁰, q = 65⁰ and r = 25⁰

• p = 25⁰, q = 32.5⁰ and r = 57.5⁰

• p = 25⁰, q = 57.5⁰ and r = 32.5⁰

• p = 25⁰, q = 57.5⁰ and r = 32.5⁰

O is the centre and PT is a tangent to the circle at T.

AOT and BOP are straight lines.

Find the values of a and b.

• a = 85⁰, b = 80⁰

• a = 80⁰, b = 80⁰

• a = 85⁰, b = 85⁰

• a = 80⁰, b = 85⁰

O is the centre, PA is a tangent to the circle at A.

AOC and PBC are straight lines.

Find the values of x, y and z.

• x = 60⁰, y = 30⁰

  and z = 90⁰

• x = 30⁰, y = 60⁰

  and z = 90⁰

• x = 60⁰, y = 60⁰

  and z = 90⁰

• x = 90⁰, y = 30⁰

  and z = 60⁰

O is the centre, PA is a tangent to the circle at A.

EOC and DOA are straight lines.

Find the values of x, y and z.

• x = 100⁰, y = 40⁰

  and z = 50⁰

• x = 140⁰, y = 20⁰

  and z = 70⁰

• x = 120⁰, y = 30⁰

  and z = 60⁰

• x = 150⁰, y = 15⁰

  and z = 75⁰

O is the centre, PA and QA are tangents to the circle at P and Q respectively.

Find the values of a, b and c.

• a = 75⁰, b = 75⁰

  and c = 60⁰

• a = 80⁰, b = 80⁰

  and c = 50⁰

• a = 45⁰, b = 45⁰

  and c = 30⁰

• a = 90⁰, b = 90⁰

  and c = 30⁰

O is the centre, PA and QA are tangents to the circle at P and Q respectively.

Find the values of a, b and c.

• a = 11.5⁰, b = 75⁰

  and c = 37.5⁰

• a = 23⁰, b = 90⁰

  and c = 67⁰

• a = 23⁰, b = 90⁰

  and c = 23⁰

• a = 11.5⁰, b = 60⁰

  and c = 30⁰