Question

In Fig. 3, AP and BP are tangents to a circle with centre 0, such that AP = 5 cm and ∠APB = 60°. Find the length of chord AB.

Answer 1

Refer to the attached file.

Answer 2

Given :

AP and BP are tangents to a circle

with centre O ,

AP = 5 cm

<APB = 60° ,

AB = ?

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By, theorem

The lengths of tangents drawn from

an external point to a circle are equal .

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Here ,

AP = PB = 5cm

Now ,

In ∆APB , AP = PB

then ∆APB is a isosceles triangle.

<PAB = <PBA = x

[ Angles opposite to equal sides

are equal ]

<PAB + <PBA + <APB = 180°

[ Angle sum property ]

=> x + x + 60° = 180°

=> 2x = 180 - 60

=> 2x = 120°

=> x = 120/2

=> x = 60°

Therefore ,

<PAB = <PBA = <APB = 60°

Therefore ,

∆APB is an equilateral triangle.

AP = PB = AB = 5 cm

Chord ( AB ) = 5 cm

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