Circle Properties and Terminology

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Circle Properties and Terminology — Free MYP3 Mathematics Practice Questions

1QuestionDrawing Circles with Compass and RulerConcept Practice

2 marks~3 minCriterion A

The diagram shows a circle with centre

O

. Points

A

and

B

lie on the circumference, connected by a straight line segment. Point

C

also lies on the circumference, connected to

O

by a straight line segment.

Identify the centre, the radius, and the chord shown in the diagram. [1]

Explain why

OC

is a radius but

AB

is not. [1]

Solutions

2QuestionExploring Tangents and Secants IntroductoryAssessment Practice

6 marks~9 minCriterion D

A satellite dish has a circular base with centre

O

and radius

1.5 \text{ m}

. A technician stands at point

P

, which is

4 \text{ m}

from

O

. Support cables run from

P

to points

A

and

B

on the edge of the dish, where

PA

and

PB

are tangents to the circle.

Calculate the length of cable

PA

. [2]

The technician measures

OP

4 \text{ m}

, but this measurement has an error of

\pm 5 \text{ cm}

. Calculate the range of possible cable lengths and explain what this means for the installation. [3]

The dish is slightly oval rather than circular. Explain one way this shape difference affects the reliability of the cable length calculated in part (a). [1]

Solutions

3QuestionExploring Tangents and Secants IntroductoryAssessment Practice

6 marks~9 minCriterion B

Point

P

lies outside a circle. Two tangent segments are drawn from

P

to the circle, touching it at points

A

and

B

.

The table below shows measurements from four different circles.

Circle 1	$PA = 5$ cm	$PB = 5$ cm
Circle 2	$PA = 7$ cm	$PB = 7$ cm
Circle 3	$PA = 9$ cm	$PB = 9$ cm
Circle 4	$PA = 12$ cm	$PB = 12$ cm

State a conjecture about the lengths of two tangent segments drawn from the same external point to a circle. [1]

A fifth circle has an external point

Q

, with tangent segments

QX = 8

cm and

QY = 8

cm. Explain whether this observation supports your conjecture. [2]

The diagram shows point

P

outside a circle with centre

O

. Tangent segments

PA

and

PB

touch the circle at

A

and

B

. Analyse the triangles

OAP

and

OBP

to explain why

PA

must equal

PB

. [3]

Solutions

4QuestionExploring Tangents and Secants IntroductoryAssessment Practice

7 marks~11 minCriterion C

In the diagram,

O

is the centre of a circle and line

PT

is a tangent to the circle at point

T

, with radius

OT

drawn to the point of tangency.

Describe what a tangent to a circle is. [1]

Explain why

OT

is the shortest distance from centre

O

to line

PT

. [2]

Justify why

OT

must be perpendicular to

PT

, using the diagram provided. [4]

Solutions

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