GCSE Maths · Higher · Chapter 20: Properties of circles · Lesson 2

Tangents, chords and the alternate segment

Grades 5–8About 50 minutesNo calculator39 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/gcse-tangents-chords-and-the-alternate-segment/

NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
An angle at the circumference is $6 4^{\circ}$ . Find the angle at the centre on the same arc.
[1 mark]
Answer
A2
From chapter 19
Of the girls, 11 walk to school and 11 do not. A girl is picked. Find P(walks).
[1 mark]
Answer
A3
From chapter 16
$x = 10$ to the nearest whole number. Write the error interval for $x$ .
[1 mark]
Answer
A4
Key Stage 3
An isosceles triangle has a top angle of $14 0^{\circ}$ . Find one base angle.
[1 mark]
Answer

Grades 5–7

Your teacher works through each example with you. Then try the one beside it.

Example 1

Tangent $P T$ , centre $O$ . Find $x$ .

Not drawn accurately

Hint A tangent meets the radius at

9 0^{\circ}

B1
Tangent $P T$ , centre $O$ . Find $x$ .
[3 marks]
Not drawn accurately
Answer

Example 2

Tangent $S A T$ . Find angle $A B C$ , with reasons.

Not drawn accurately

Hint Use the alternate segment theorem.

B2
Tangent $S A T$ . Find angle $A B C$ , with reasons.
[3 marks]
Not drawn accurately
Answer

Grades 5–7

C1
Centre $O$ , $O M ⊥ A B$ . Find $A B$ .
[3 marks]
Not drawn accurately
Answer
C2
Tangent $P T$ , centre $O$ . Find angle $T P O$ .
[2 marks]
Not drawn accurately
Answer

C3
Tangents $P A$ and $P B$ . Find the length $P A$ .
[3 marks]
Not drawn accurately
Answer
C4
Tangent $A T$ , centre $O$ . Find angle $B A T$ .
[3 marks]
Not drawn accurately
Answer

Grades 6–8

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can use tangent and radius at $9 0^{\circ}$ .
I can use equal tangents and chords.
I can use the alternate segment.

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