Question

Ab is a diameter and acis a chord of a circle such that angle bac = 30 . If the tangent at c intersects ab produced at d , then prov that bc= bd

Answer 1

Answer:

Step-by-step explanation:

Angle BAC = 30 deg (given)

Angle ACB = 90 deg (theorem)

If O is the center then Angle OCD = 90 (CD is a tangent)

Angle ACO = 30 deg (isoceles triangle , two sides = radius)

Therefore Angle ACD = 90 + 30 = 120 deg

Therefore Angle ADC = 180 - 120 - 30 = 30 deg

Angle BCD = 120 - 90 = 30 deg

Therefore Triangle BCD is isoceles, so BC = BD.

Answer 2

Step-by-step explanation:

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