Question

The length of a tangent from a point A at distance 5 cm from the center of the circle is 4 cm find the radius of the circle

Answer 1

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AB is a tangent drawn on this circle from point A. ∴ OB ⊥ AB OA = 5cm and AB = 4 cm (Given) In ΔABO, By Pythagoras theorem in ΔABO, OA2 = AB2 + BO2 ⇒ 52 = 42 + BO2 ⇒ BO2 = 25 - 16 ⇒ BO2 = 9 ⇒ BO = 3 ∴ The radius of the circle is 3 cm.Read more on Sarthaks.com - https://www.sarthaks.com/2664/the-length-tangent-from-point-distance-from-the-centre-the-circle-find-the-radius-the-circle

Answer 2

Answer:

AB is a tangent drawn on this circle from point A.



∴ OB ⊥ AB 

OA = 5cm and AB = 4 cm (Given) 

In ΔABO, 

By Pythagoras theorem in ΔABO, 

OA2 = AB2 + BO2 

⇒ 52 = 42 + BO2 

⇒ BO2 = 25 - 16 

⇒ BO2 = 9 

⇒ BO = 3 

∴ The radius of the circle is 3 cm.

Step-by-step explanation:

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