If a radius of a circle bisects a chord which is not a diameter, then ______
2 answers:
Answer:
the radius is perpendicular to the chord.
Step-by-step explanation:
The geometry is drawn in the image shown below in which AB is the chorh and O is the centre of the circle. Om is the radius which bisects the chord.(Given) So, AN = NB
From the image, considering ΔAON and ΔBON,
AO = BO (radius of circle)
AN = NB (given)
ON = ON (common)
So,
<u>ΔAON ≅ ΔBON</u>
Hence, ∠ANO = ∠BNO
Also, ∠ANO + ∠BNO = 180° (Linear Pair)
So,
∠ANO = ∠BNO = 90°
<u>Hence, it is perpendicular to the chord.</u>
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