Circle theorems: alternate segment

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The line at A touches the circle. Which marked angle is bigger, at A or at C?

ABC They are equal

The angle between a tangent and a chord equals the angle in the alternate segment

Which angle is equal?

ABCThe marked angle Angle C

Find x.

55°xABC
x =55°
alternate segment

Find x.

x48°ABC
x =48°
alternate segment

Find x.

55°xABC
x =55°
alternate segment

Find x.

2x70°ABC
2x =70°
alternate segment
x =35°

Circle theorems: alternate segment worksheet, page 1

Answer sheet

ABC
  1. The tangent at A makes 50° with AB on one side and 60° with AC on the other. Find angle BAC. 70°

  2. Why is the angle between a tangent and a diameter 90°? The angle in a semicircle is 90°

  3. The tangent at A makes 46° with AB. AC = BC. Find angle CAB. Angle ACB = 46°, so (180° − 46°) ÷ 2 = 67°

  1. The line through A is a tangent. Find angle x.

    x = 58°
    ABC58°x
  2. The line through A is a tangent. Find x.

    x = 27
    ABC2x + 1064°
  3. AC = BC. Find angle CAB.

    64°
    ABC52°
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