Maharashtra Board Class 8 Maths part 2 Chapter 17 Circle Chord and Arc PDF Download

Practice Set 17.2

1. The diameters PQ and RS of the circle with centre C are perpendicular to each other at C. State, why arc PS and arc SQ are congruent. Write the other arcs which are congruent to arc PS

2. In the adjoining figure O is the centre of the circle whose diameter is MN. Measures of some central angles are given in the figure. Hence find the following

(1) m∠AOB and m∠COD

(2) Show that arc AB ≅ arc CD.

(3) Show that chord AB ≅ chord CD

Teacher's Note

When two diameters are perpendicular, they divide the circle into equal parts. Think of a pizza cut into 4 equal slices - each slice has the same angle at the center.

Exam Trick

Remember: Equal central angles mean equal arcs. Equal arcs mean equal chords. This is like a chain - if the first thing is equal, everything connected to it is also equal.

Points to Remember

Perpendicular diameters divide a circle into 4 equal arcs of 90° each.
Congruent arcs have equal measures in degrees.
If two arcs are congruent, their chords are also congruent.
Central angle measure equals arc measure.

Answers

Practice Set 17.1

1. 6.5 cm

2. 7 cm

3. 15 cm

4. 8 cm

Practice Set 17.2

1. (1) Because the arcs are of equal measures, that is 90° each.

(2) arc PS ≅ arc PR ≅ arc RQ

2. (1) m∠AOB = m∠COD = 45°

(2) arc AB ≅ arc CD because the arcs are of equal measures that is 45° each.

(3) chord AB ≅ chord CD because corresponding chords of congruent arcs are congruent.

Teacher's Note

In the second problem, we use the property that equal central angles give us equal arcs. This is used in many real designs like wheel rims and clock faces.

Exam Trick

Always write the angle measure first, then the arc measure. If central angles are equal, write the arc measures and chord lengths as equal immediately - no more work needed!

Points to Remember

Central angle and its arc have the same measure in degrees.
If two central angles are equal, their arcs are equal.
If two arcs are equal, their chords are equal.
A diameter divides a circle into two semicircles of 180° each.

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