2) If chords AB and CD of congruent circles subtend equal angles at their centres, then: a. AB = CD b. AB > CD c. AB < AD d. None of the above
Answers
Given : chords AB and CD of congruent circles subtend equal angles at their centres,
To Find : Correct option
a). AB = CD
b. AB > CD
c. AB < AD
d. None of the above
Solution:
Using cosine rule
Chord length of circle = √r² + r² - 2r²Cosα
r = radius of circle
α = angle subtended at center by chord
= √2r²(1- Cosα)
= √2r²2sin²(α/2)
= 2rsin(α/2)
congruent circles have same radii
chords AB and CD subtend equal angles at their centres,
angle are also Equal
Hence AB = CD = 2rsin(α/2
Hence AB = CD
option A is correct
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Answer:
AB=CD
Step-by-step explanation:
AB=CD is the answer
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