In Fig. 10.2, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD, respectively. If ∠POQ = 150º, then ∠APQ is equal to
a. 30º
b. 75º
c. 15º
d. 60º
Solution:
We know that
Equal chords are situated at equal distance
OP = OQ
If two chords are equal, its angles are equal in a triangle
∠P = ∠Q = x
From the angle sum property in triangle OPQ
150 + x + x = 180º
By further calculation
150 + 2x = 180º
2x = 180 - 150
2x = 30º
Dividing both sides by 2
x = 15º
Here
∠APO = x + ∠APQ = 90º
So we get
∠APQ = 90 - 15 = 75º
Therefore, ∠APQ is equal to 75º.
✦ Try This: AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD, respectively. If ∠POQ = 140º, then ∠APQ is equal to
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10
NCERT Exemplar Class 9 Maths Exercise 10.1 Sample Problem 2
In Fig. 10.2, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD, respectively. If ∠POQ = 150º, then ∠APQ is equal to a. 30º, b. 75º, c. 15º, d. 60º
Summary:
In Fig. 10.2, AB and CD are two equal chords of a circle with centre O. OP and OQ are perpendiculars on chords AB and CD, respectively. If ∠POQ = 150º, then ∠APQ is equal to 75º
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