prove that the line drawn through the centre od the circle to bisect the chord is perpendicular to the circle.
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Statement : The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
Given : A chord PQ of a circle C ( O, r ) and L is the mid - point of PQ.
To prove : OL ⊥ PQ
Construction : Joint OP and OQ.
PROOF :
In ∆OLP and ∆OLQ,
OP = OQ . (radii of same circle)
PL = QL . (given)
OL = OL . (common)
ΔOLP ≅ ΔOLQ . (SSS)
Also,
∠OLP + ∠OLQ = 180° (linear pair)
∠OLP = ∠OLQ = 90°
Hence, OL ⊥ PQ.
Given : A chord PQ of a circle C ( O, r ) and L is the mid - point of PQ.
To prove : OL ⊥ PQ
Construction : Joint OP and OQ.
PROOF :
In ∆OLP and ∆OLQ,
OP = OQ . (radii of same circle)
PL = QL . (given)
OL = OL . (common)
ΔOLP ≅ ΔOLQ . (SSS)
Also,
∠OLP + ∠OLQ = 180° (linear pair)
∠OLP = ∠OLQ = 90°
Hence, OL ⊥ PQ.
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