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5. Solve the following questions : (Any One)(1) In the given figurePoint O is the centre of the circle.Show that L AOC =LAFC +LAECR and A-0-C such that |
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Answer» Given:In the given figure O is the centre of the circle.To Prove:∠AOC=∠AFC+∠AECProof:In ΔBEC using exterior angle theorem.Exterior angle theorem property:Sum of two interior angle of triangle is equal to opposite exterior angle. So, we get∠ABC=∠AEC+∠BCD Double the above equation both sides2∠ABC=2∠AEC+2∠BCDAngle subtended on circle is half angle subtended at centre. 2∠ABC=∠AOC∠AOC=∠AEC+∠BCD+∠AEC+∠BCD∠AOC=∠AEC+∠BCD+∠ABCBut∠ABC=∠ADC(∴Angles subtended on same arc are equal)∠AOC=∠AEC+∠BCD+∠ADCIn ΔFDC using exterior angle theorem.∠AFC=∠BCD+∠ADC∴∠AOC=∠AEC+∠AFCHenceproved,∠AOC=∠AFC+∠AEC |
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