In Fig. 10.1, two congruent circles have centres O and O′. Arc AXB subtends an angle of 75º at the centre O and arc A′ Y B′ subtends an angle of 25º at the centre O′. Then the ratio of arcs A X B and A′ Y B′ is:
a. 2 : 1
b. 1 : 2
c. 3 : 1
d. 1 : 3
Solution:
Let us use the area of arc formula
Area of arc = 1/2 r² θ
In case I
Area of AXB = 1/2 r² (75º)
In case II
Area of A’YB’ = 1/2 r² (25º)
So the ratio will be
Required ratio = Area of AXB/ Area of A’YB’
Substituting the values
= 1/2 r² (75º)/ 1/2 r² (25º)
= 75/25
= 3
Therefore, the ratio of arcs A X B and A′ Y B′ is 3: 1.
✦ Try This: PQ and RS are two equal chords of a circle with centre O. OA and OB are perpendiculars on chords PQ and RS, respectively. If ∠AOB = 180º, then ∠PAB is equal to
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10
NCERT Exemplar Class 9 Maths Exercise 10.1 Sample Problem 1
In Fig. 10.1, two congruent circles have centres O and O′. Arc AXB subtends an angle of 75º at the centre O and arc A′ Y B′ subtends an angle of 25º at the centre O′. Then the ratio of arcs A X B and A′ Y B′ is: a. 2 : 1, b. 1 : 2, c. 3 : 1, d. 1 : 3
Summary:
In Fig. 10.1, two congruent circles have centres O and O′. Arc AXB subtends an angle of 75º at the centre O and arc A′ Y B′ subtends an angle of 25º at the centre O′. Then the ratio of arcs A X B and A′ Y B′ is 3: 1
☛ Related Questions:
- In Fig. 10.2, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars . . . .
- AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from t . . . .
- In Fig. 10.3, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to: a. 2 cm, b . . . .
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