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  •   In fig. (2) AB is a chord of length 8 cm of a circle of radius 5 cm. The tangents to the circle at A and B intersect at P. Find the length of AP <img alt="" src="https://cdn.entrance360.com/media/uploads/2020/05/07/dgetr.PNG"

 

In fig. (2) AB is a chord of length 8 cm of a circle of radius 5 cm. The tangents to the circle at A and B intersect at P. Find the length of AP

 

 

 
 
 
 
 

Answers (1)

Construct OC \perp AB\\\\  and extend OC up to P 

In \Delta AOC and \Delta AOP \\\\ \angle a = \angle c \left \{ 90 \degree \right \}\\\\ \angle O = \angle O \left \{ common \right \}\\\\ \Delta AOC \sim \Delta AOP \left \{ by \: \: AA\: \: similarity \right \} \\\\ Then \: \: \: AC = \frac{AB }{2}=4cm \ \\ So \ OC = 3\ c m \left \{ by \: \: phythagoras theorem \right \}

In \: \: \Delta AOC \ and\ \Delta POA \\\\ \frac{AO}{AP} = \frac{OC }{AC}\\\\ \frac{5}{AP} = \frac{3}{4} \\\\ AP = 20/3 cm

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