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

Mathematics

2 answers:

elena-14-01-66 [18.8K]3 years ago

4 0

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.

ch4aika [34]3 years ago

3 0

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,

ΔAON ≅ ΔBON

Hence, ∠ANO = ∠BNO

Also, ∠ANO + ∠BNO = 180° (Linear Pair)

So,

∠ANO = ∠BNO = 90°

Hence, it is perpendicular to the chord.

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