Circle theorems: tangents

The Maths Habit

A bike wheel stands on a flat road. What angle does the spoke pointing straight down make with the road?

90°

A tangent meets a radius at 90°

What is the angle?

Between a tangent and the radius it touches 90°

PT is a tangent. Find x.

O30°xTP
Angle OTP =90°tangent meets
radius at 90°
x = 180 − 90 − 30
x =60°

PT is a tangent. Find x.

Ox52°TP
Angle OTP =90°tangent meets
radius at 90°
x = 180 − 90 − 52
x =38°

PT is a tangent. Find x.

O30°xTP
Angle OTP =90°tangent meets
radius at 90°
x = 180 − 90 − 30
x =60°

PT is a tangent. Find x.

OxxTP
Angle OTP =90°tangent meets
radius at 90°
2x = 180 − 90
x =45°

Circle theorems: tangents worksheet, page 1

Answer sheet

OPAB

  1. OA = 5 cm and OP = 13 cm. Find PA. 12 cm

  2. Angle APB is 70°. Find angle OAB. 35°

  3. Angle APB is 58°. Find angle AOB. 360 − 90 − 90 − 58 = 122°

  1. PT is a tangent, centre O. Find angle x.

    x = 56°
    OTP34°x

  2. PA and PB are tangents, centre O. Find angle y.

    y = 136°
    ABOP44°y

  3. OT is 8 cm and OP is 17 cm. Find PT.

    PT = 15 cm
    OTP
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