if the hypotenuse AC Of a right angle triangle abc is of lenght 2ab prove angle BAC is equal to 2angle acb
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Step-by-step explanation:
Using angle sum property of triangle ABC
∠ABC + ∠BAC + ∠ACB = 180°
⇒ 90° + ∠BAC + 2∠BAC = 180°
⇒ 3∠BAC = 90°
⇒∠BAC = 30°
∴ ∠ACB = 2 × 30° = 60°
Similarly, it can be proved that ∠ADB = 60° and ∠BAD = 30°
∴ ∠CAD = 30° + 30° = 60°
In ∆ACD, ∠CAD = ∠ACD = ∠ADC = 60°
So, ∆ABC is an equilateral triangle.
∴ AC = CD = AD
we know that the perpendicular drawn to a side from opposite vertex bisects the side
∴ CD = 2BC
⇒ AC = 2BC [CD = AC]
Hence, proved
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