Question

if AB is a chord of a circle whose center is 0 if AOB 60 degree then prove that length of chord AB is equal to radius of circle
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Answer 1

Answer:

r

Step-by-step explanation:

Consider a circle with centre ) and AB as chord. As per question it is extending 60° at the centre. Draw a line bisecting the angle to AB meeting it at C, hence, C is the mid point of AB. Now, consider Δ OCA (Right angled at C) has ∠OAC = 60° (Since, ∠OAC = 180° - 90° - 30°). Now, Using trigonometry: cos ∠OAC = CA/OA or CA = OA x cos∠OAC. Here, OA = Radius of circle 'r' and cos∠OAC = cos60° = (1/2). Hence, CA = (r/2). Similarly, we can prove CB = (r/2). Now, AB = CA + CB, hence, AB = (r/2) + (r/2) = r. Hence, proved.