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Quiz about Maths Topic 3 Circle Geometry

Maths Topic 3: Circle Geometry Quiz

This quiz will cover basic knowledge and applications of rules in circle geometry. Diagrams may be drawn for assistance and calculators may be used. Good luck.

A multiple-choice quiz by dialga483. Estimated time: 5 mins.

Author
dialga483

Time
5 mins

Type
Multiple Choice

Quiz #
365,978

Updated
Dec 03 21

# Qns
10

Difficulty
Tough

Avg Score
5 / 10

Plays
224

One at a Time - Single Page

Question 1 of 10

1. "Equal arcs subtend equal angles at the centre of the circle", is a rule associated with circle geometry. Which other geometric part of a circle can be associated with this rule? Hint

Secant

Chord

Tangent

Radius

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Question 2 of 10

2. The quadrilateral ABCD lies within a circle, where points A, B and D all lie on the circumference and point C is the centre of the circle. If acute angle BCD is equal to 80 degrees, what is the size of acute angle BAD at the circumference? Hint

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Question 3 of 10

3. Two scalene triangles, ABC and DEC lie within a circle, where they both touch at point C which lies above the centre of the circle, which is point O. Lines are drawn from the centre at O, forming equal radii AO and AD. Points A, B, D and E all lie on the circumference. From the two triangles, which corresponding pair of angles are equal? Hint

Angles BCA and CDE

Angles CBA and ECD

Angles BAC and CED

Angles CBA and CED

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Question 4 of 10

4. AB is the diameter of a circle. If BC=2cm and AB=9cm, then what is the exact length of AC? Hint

sqrt(77) cm

sqrt(65) cm

sqrt(72) cm

sqrt(56) cm

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Question 5 of 10

5. AB and CD are chords of a circle that intersect at point E. If AB=12.3cm, EB=2.7cm and DE=10.6cm, then what is the value of EC? (correct to 1 dec pl) Hint

3.1cm

1.9cm

3.5cm

2.4cm

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Question 6 of 10

6. ABCD is a cyclic quadrilateral that lies inside a circle. If angle ABC is equal to 56, then what is the value of angle ADC? Hint

124

146

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Question 7 of 10

7. The tangent to a circle is perpendicular to which other part of the circle at the point of contact? Hint

Arc

Secant

Radius

Chord

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Question 8 of 10

8. One tangent to the circle at point A is 7cm long and meets at the external
point C. The second tangent to the circle at point B also meets at the external point C. How long is the tangent BC? Hint

3.5cm

7cm

10.5cm

14cm

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Question 9 of 10

9. AB and AC are chords of a circle with a tangent at A. The angle between the tangent and the chord AC is equal to which other angle? Hint

Angle ABC

Angle ACB

Angle BAC

Exterior angle at B

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Question 10 of 10

10. AB is a tangent to a circle, where point A lies on the circle and point B is an external point. Points C and D also lie on the circle, forming lines BC and BD, where BC is smaller than BD and the point C also lies on the line BD. CD is 1.3 cm and BC is 1.7 cm. What is the length of AB, correct to 1 decimal place? Hint

2.3 cm

2.1 cm

1.5 cm

1.7 cm

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Quiz Answer Key and Fun Facts

1. "Equal arcs subtend equal angles at the centre of the circle", is a rule associated with circle geometry. Which other geometric part of a circle can be associated with this rule?

Answer: Chord

If two chords are equal, then they will subtend equal angles at the centre of the circle. This rule is similar to rule for equal arcs.

Answer: 40

To solve this question, we can use the rule "angles at the circumference are half the angles at the centre". Since the angle at the centre is 80, we can halve this to find the angle at the circumference, which is 40.

Answer: Angles CBA and CED

If we let angle AOD at the centre of the circle be equal to x, then we can use the rule "angles at circumference are half the angles at the centre". This rule shows that angles CBA and CED are both equal to x/2. Therefore, the pair of angles are equal. The pair of angles can also be found using the rule, "angles in the same segment of a circle are equal".

4. AB is the diameter of a circle. If BC=2cm and AB=9cm, then what is the exact length of AC?

Answer: sqrt(77) cm

Since AB is a diameter, this splits the circle into 2 semi-circles. We can then use the rule "angles in a semi circle are right angles" to show that triangle ABC is right angled at C. We can then use Pythagoras's theorem to work out the remaining side.
So
AC^2=9^2-2^2
AC^2=77
Therefore, AC=sqrt(77)cm

5. AB and CD are chords of a circle that intersect at point E. If AB=12.3cm, EB=2.7cm and DE=10.6cm, then what is the value of EC? (correct to 1 dec pl)

Answer: 2.4cm

To solve this question, we use the rule "the products of intersecting chords are equal". In this case, (AE x EB) = (DE x EC).
AE = AB-EB
= 12.3 - 2.7
= 9.6
So using information given,
10.6EC = (9.6 x 2.7)
EC = (9.6 x 2.7)/10.6
EC = 2.445283019
Therefore, EC = 2.4cm

6. ABCD is a cyclic quadrilateral that lies inside a circle. If angle ABC is equal to 56, then what is the value of angle ADC?

Answer: 124

For any cyclic quadrilateral, opposite angles are supplementary, meaning they add up to 180. In this case, angle ABC is opposite to angle ADC.
So
Angle ADC = 180 - angle ABC
= 180 - 56
= 124

7. The tangent to a circle is perpendicular to which other part of the circle at the point of contact?

Answer: Radius

The tangent is a straight line that touches the circle at a single point. The radius of the same circle forms a right angle at the point of contact. Therefore, this makes the tangent perpendicular to the radius at the point of contact.

8. One tangent to the circle at point A is 7cm long and meets at the external point C. The second tangent to the circle at point B also meets at the external point C. How long is the tangent BC?

Answer: 7cm

We can solve this question using the rule "the tangents of a circle that meet at an external point are equal". Therefore, since both tangents meet at the same external point, they are both 7cm.

9. AB and AC are chords of a circle with a tangent at A. The angle between the tangent and the chord AC is equal to which other angle?

Answer: Angle ABC

This question can be solved using the rule "the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment". Therefore, the angle between the tangent and the chord AC, is equal to angle ABC.

Answer: 2.3 cm

To find the length of the side, we need to use the rule
(tangent)^2 = (ext length)x(whole length)
In this case
AB^2= BC x BD
AB^2= 1.7 x (1.7+1.3)
AB^2= 1.7 x 3
AB^2= 5.1
AB= sqrt(5.1)
AB= 2.258317958
Therefore, AB = 2.3 cm

Source: Author dialga483

This quiz was reviewed by FunTrivia editor rossian before going online.
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