# If a radius of a circle bisects a chord which is not a diameter, then ______

2 answers

###### Question:

If a radius of a circle bisects a chord which is not a diameter, then ______

## Answers

Frst, some notation. Let AB be a chord on circle O, and let CD be a diameter of O that passes through AB at M.

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 = NBFrom the image, considering ΔAON and ΔBON, AO = BO (radius of circle)AN = NB (given)ON = ON (common)So, ΔAON ≅ ΔBONHence, ∠ANO = ∠BNOAlso, ∠ANO + ∠BNO = 180° (Linear Pair)So, ∠ANO = ∠BNO = 90°Hence, it is perpendicular to the chord.

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