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Answer :
Length of chord, AB = 5 cm
Solution :
Given,
AP and BP are tangents to a circle with centre O.
AP = 5 cm
We know that,
Two tangents drawn from external point to a circle are equal.
⇒ PA = PB = 5 cm
In ∆APB,
∠APB = 60°
Angles opposite to equal sides in a traingle are equal.
⇒ ∠PAB = ∠PBA
Sum of angles in a triangle = 180°
∠PAB + ∠PBA + ∠APB = 180°
∠PBA + ∠PBA + 60 = 180
2∠PBA = 120
∠PBA = 60°
⟶ ∠PBA = ∠PAB = 60°
It shows that all angles in the triangle are same i.e, 60°
⇛ ∆APB is equilateral.
Thus, all sides of triangle are equal.
AB = 5 cm
∴ Length of chord = 5 cm