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In this section we will discuss Theorems on Chord. |
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1) BC = PQ | 1) Given |
2) OP = AB | 2) Radius of a circle |
3) OQ = AC | 3) Radius of a circle |
4) ΔPOQ = ΔBAC | 4) SSS Postulate |
5) ∠POQ = ∠BAC | 5) CPCTC |
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1) OP = OQ | 1) Radii of the same circle. |
2) OM = OM | 2) Reflexive (common) |
3) ∠OMP = ∠OMQ | 3) Each 900 |
4) ΔPMO = ΔQMO | 4) HL postulate(RHS) |
5) PM = MQ | 5) CPCTC |
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1) AB = AC | 1) Given |
2) ∠BAM = ∠CAM | 2) Given |
3) AM = AM | 3) Reflexive (Common) |
4) ΔBAM = ΔCAM | 4) SAS Postulate |
5) BM = CM and ∠BMA = ∠CMA | 5) CPCTC |
6) ∠BMA + ∠CMA = 900 | 6) Linear pair angles |
7) AM = BM and ∠BMA = ∠CMA = 900 | 7) From (6) |
8) AM is the perpendicular bisector of BC | 8) Definition of perpendicular bisector. |
9) AM passes through the center O. | 9) Perpendicular bisector of a chord always passes through the center. |
Russia-Ukraine crisis update - 3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.