AB and BC are two equal chords of a circle of radius 20cm. D is a point on AB produced such that CD is perpendicular to AD. if angle ABC = 120degree, then find BD. ans= 10cm. approach please..

Question

Answer 1

But CD is perpendicular to AD . How ?

Answer 2

But CD is perpendicular to AD . How ?

Answer 3

Let the center of the circle be O. Join OA, OB and OC. Triangle AOB is congruent to triangle COB (SSS). Since angle ABC is 120, angle ABO is 60. Since BO = AO, angle BAO is also 60. So, angle AOB is 60 degrees. AOB is an equilateral triangle. So, AB = AO = radius = 20 cm. In triangle BCD, angle B = 180 - 60 - 60 = 60 degrees
BC = 20 cm
So, BD = BC cos 60 = 20 * 1/2 = 10 cm

Answer 4

Let the center of the circle be O. Join OA, OB and OC. Triangle AOB is congruent to triangle COB (SSS). Since angle ABC is 120, angle ABO is 60. Since BO = AO, angle BAO is also 60. So, angle AOB is 60 degrees. AOB is an equilateral triangle. So, AB = AO = radius = 20 cm. In triangle BCD, angle B = 180 - 60 - 60 = 60 degrees
BC = 20 cm
So, BD = BC cos 60 = 20 * 1/2 = 10 cm

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AB and BC are two equal chords of a circle of radius 20cm. D is a point on AB produced such that CD is perpendicular to AD. if angle ABC = 120degree, then find BD. ans= 10cm. approach please..