Question

if figure,pa and pb are tangents such that PA =9 cm and triangle apb =60 find ab
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Answer 1

Answer:

The length of the chord AB is 9 cm.

Step-by-step explanation:

It is given that,

PA and PB are tangents to a circle from external point P touching the circle at A and B .

PA = 9 cm  

∠APB = 60°

We know that if two tangents are drawn to a circle from one external point, then they have equal tangent segments.

∴ PA = PB = 9 cm

⇒ ∠PBA = ∠PAB ….. [angles opposite to equal sides are equal] ….. (i)

Now consider ΔPAB and applying the angle sum property, we get

∠PBA + ∠PAB + ∠APB = 180°

⇒ ∠PBA + ∠PAB + 60° = 180°

⇒ 2 * ∠PBA = 180° - 60° …… [from eq. (i)]

⇒ 2 * ∠PBA = 120°  

⇒ ∠PBA = 120°/2

⇒ ∠PBA = 60°

∴ ∠PBA = ∠PAB = ∠APB = 60°

Since all the 3 angles of ΔPAB is equal to 60°, therefore, we get that ΔPAB is an equilateral triangle.

We know that all the sides of an equilateral triangle are equal to each other.

∴ PA = PB = AB = 9 cm

Thus, the length of the chord AB of the given circle is 9 cm.