1
Question
The following figure shows a circle with centre O.
If OP is perpendicular to AB, prove that AP =BP.
The following figure shows a circle with centre O.
If OP is perpendicular to AB, prove that AP =BP.
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Solution
AB is the chord of the circle.
join A and B to O
in triangle APO and BPO
AO = BO (radii of the same circle)
∠APO = ∠BPO (given OP ⊥ AB)
OP = OP (common side)
therefore two triangles are congruent by SAS congruency
AP = BP (cpct)
AB is the chord of the circle.
join A and B to O
in triangle APO and BPO
AO = BO (radii of the same circle)
∠APO = ∠BPO (given OP ⊥ AB)
OP = OP (common side)
therefore two triangles are congruent by SAS congruency
AP = BP (cpct)
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