Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD. Is the given statement true or false and justify your answer
Solution:
It is given that
AB and CD are the chords of a circle at a distance of 4 cm from the centre
We know that
OM and ON are perpendiculars of 4 cm from the centre O to AB and CD
It bisects AB and CD
Here
AM = 1/2 AB
DN = 1/2 DC
∠OMA = ∠OND = 90º
In between the triangles AOM and DON
OM = ON = 4 cm [Given]
∠OMA = ∠OND = 90º
OA = OD (radii of the same circle)
From the RHS rule
Δ AOM ≅ Δ DON
AM = DN and AB = DC
Therefore, the statement is true.
✦ Try This: In Figure O is the centre of the circle. If ∠OAB = 40° and ∠OCB = 30°, find ∠AOC.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10
NCERT Exemplar Class 9 Maths Exercise 10.2 Problem 1
Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD. Is the given statement true or false and justify your answer
Summary:
The statement “Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD” is true
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