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triangles ABC is inscribed in a circle and AB=AC the bisector of angle ABC meets the tangent from A at D. Prove that AD and BC are parallel?

and also triangles ADC is isocles

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  • 4 years ago
    Favorite Answer

    Join AE to E the mid point of BC. Because AB = AC AE must also be perpendicular to BC. So it must pass through the center of the circumscribed circle of triangle ABC. As AD is tangent ∠EAD must be a right angle. We have already proved that ∠AEC is a right angle As these internal angles of BC and AD formed by transverse AE add to two right angles AD||BC. Hence proved.

    As AD||BC

    ∠DBC = ∠BDA (alternate angles)

    but ∠DBC = ∠DBA (given)

    so ∠DBA = ∠BDA in the ΔABD, hence AB = AD but AB = AC (given so AC = AD hence ΔACD is isosceles..

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  • Anonymous
    4 years ago

    Due to have two of the same sides, the triangle has to be an isosceles.

    The reason AD and BC are parallel as the bisector produces a line that is 90 degrees with the tangent line and with side BC

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  • 4 years ago

    no picture is given. the question is exactly what i have written

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