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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
8.7 Circles

Radius: A line joining the centre to any point on the circle.
Diameter: Two times the radius is the diameter.
Chord: A line segment joining any two points on the circle is chord.
Major Arc and Minor Arc: Any two points A and B of a circle divide the circle into two points. If the two parts are unequal, the smaller part is called minor arc and the larger part is called major arc.

A circle divides the plane into three parts, its interior exterior and the circle itself.
The circle along with its interior is called the circular region.
A chord divides a circular region into two parts called the segments of the region.
The smaller segment is called the minor segment and the larger segment is called the major segment

Theorem 1: In a circle, the perpendicular from the center to the chord bisects the chord.

Theorem 2: Chords of a circle which are equidistant from the centre are equal.

Given: OM = ON (radii of the circle)
To prove: AB = CD
Construction: Join AO and CO
Proof: Consider triangles AMO and CNO
OM = ON
Angle M = Angle N = 90o
Angle AOM = CON (common angle)
Hence triangles AMO and CNO are similar.
Hence AB = CD


Directions: Solve the following.
Q 1: Find the length of the chord if the radius of circle is 13 cm and distance from the centre is 5 cm.
Answer:

Q 2: PQ and RS are two parallel chords of a circle whose radius is 10 cm. If PQ = 16 cm and RS = 12 cm, find the distance between the chords if they lie on the same side of the centre.
Answer:

Q 3: PQ and RS are two parallel chords of a circle whose radius is 10 cm. If PQ = 16 cm and RS = 12 cm, find the distance between the chords if they lie on the opposite side of the centre.
Answer:

Q 4: Find the missing angle.

260 degrees
100 degrees
150 degrees

Q 5: Find the missing angle.

Both angles are 35 degrees.
Both angles are 40 degrees.
Both are 50 degrees

Q 6: In a circle of radius 5 cm, AB and AC are two chords such that AB = AC = 6cm, find the length of the chord BC.
Answer:

Q 7: Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other on the same side of the centre. If the distance between the chords is 3 cm, find the radius of the circle.
Answer:

Q 8: AB and CD are two equal chords to a circle of centre O. If OM is perpendicular to AB and ON is perpendicular to CD. Prove that angle OMN = angle ONM
Answer:

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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