1
Question
The given figure shows two chords drawn on either side of the diameter, making equal angles with the diameter. Calculate the length of the other chord if the length of one chord is 18 units. [2 marks]
Open in App
Solution
Take O as the centre of the circle and name the chords as AB and AC.
Make OP such that OP ⊥ AB & AP = PB
Similarly, OQ ⊥ AC & AQ = QC
Given that, AB = 18 units [1 mark]
Consider ∆OPA and ∆OQA,
∠PAO = ∠QAO = x° (Given)
AO = AO (Common side)
∠APO = ∠AQO = 90° (Right angles)
∴ ∆OPA ≅ ∆OQA by AAS congruence.
So, AP = AQ
Hence, AB = AC = 18 units [1 mark]
Take O as the centre of the circle and name the chords as AB and AC.
Make OP such that OP ⊥ AB & AP = PB
Similarly, OQ ⊥ AC & AQ = QC
Given that, AB = 18 units [1 mark]
Consider ∆OPA and ∆OQA,
∠PAO = ∠QAO = x° (Given)
AO = AO (Common side)
∠APO = ∠AQO = 90° (Right angles)
∴ ∆OPA ≅ ∆OQA by AAS congruence.
So, AP = AQ
Hence, AB = AC = 18 units [1 mark]
Suggest Corrections
0
Similar questions