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Show that if two chords of a circle bisects each other they must be diameters of the circle. |
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Answer» Let AB and CD be two chords intersecting at point O. Join AC and BD.NowΔAOC≈ΔBOD⇒AC=BD⇒∧AC =∧ BD-----------(1)Now,ΔAOD≈ΔBOC⇒AD=BC⇒∧AD=∧BC--------(2) (1)+(2)⇔∧AC+∧AD =∧BD+∧BC⇒ ANGLE "CAD"= ANGLE "CBD"Then CD divides the circle into two equal parts thus CD is a diameterSimilarly AB is also the diameter and they both meet at point OThus they bisect each other |
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