Question

in a figure AP and bp are the tangents of the circle with Centre O such that a b is equal to 5 cm and angle b is equal to 60 degree then find the length of the chord a b

Answer 1

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Answer 2

Answer:

Length  of AB = 5 cm

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the problem :

AP = BP = 5 cm ( Tangents drawn to the same chord from the same point are equal in length)

⇒ ∠PAB = ∠PBA ( Angles opposite to equal sides are equal to each other)

∠APB = 60°

Using angles sum property of triangle in ΔAPB

⇒ ∠APB + ∠PBA + ∠PAB = 180

⇒ ∠PAB + ∠PAB = 180 - 60

⇒ 2∠PAB = 120

⇒ ∠PAB = 60°

⇒ ∠PBA = ∠PAB = 60°

Now, in ΔAPB, each angle is of 60°. So, the ΔAPB is an equilateral triangle.

⇒ AP = BP = AB = 5 cm

Hence, Length  of AB = 5 cm