Circles Practice 3: Combined Problems And Proofs

Practise focused skills from Circles

MathematicsGrade 10Mixed10 questions20 min

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Section A: Combined Reasoning · 5 questionsSection B: Proof and Error Analysis · 5 questions

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Section A: Combined Reasoning

Build and apply the key ideas for this part of the chapter.

Choose the best answer for each question.

Question 1

MediumQuestion

From point $P$ , $PA$ and $PB$ are tangents to a circle with centre $O$ . If $\angle APB=60^\circ$ , what is true about $\triangle APB$ ?

Topic: Combined Problems · Skill: Combine circle theorems with triangle geometry

Question 2

AdvancedQuestion

In a circle, $PT$ is tangent at $T$ , $OT=6$ cm and $OP=10$ cm. Which additional fact helps find $\angle OPT$ after finding $PT$ ?

Topic: Combined Problems · Skill: Combine circle theorems with triangle geometry

Question 3

EasyQuestion

Which is the best structure for a circle tangent proof?

Topic: Proof Writing · Skill: Write structured circle tangent proofs

Question 4

MediumQuestion

Which reason is valid in a tangent proof?

Topic: Proof Writing · Skill: Write structured circle tangent proofs

Question 5

MediumQuestion

A student says a line is tangent because it is close to the circle in the diagram. What is wrong?

Topic: Error Analysis · Skill: Identify invalid tangent assumptions

What this assignment covers

Combine tangent theorems with triangle geometry, proof writing and error analysis.

Skills and sections

Combine circle theorems with triangle geometry, Write structured circle tangent proofs, Identify invalid tangent assumptions, Find angles using tangent-radius relation, Find lengths using right triangles

Section A: Combined Reasoning: 5 questions
Section B: Proof and Error Analysis: 5 questions