Question
Mathematics Question on Number of Tangents from a Point on a Circle
The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Answer
Let us consider a circle centered at point O.
AB is a tangent drawn on this circle from point A.
Given that,
OA = 5 cm and AB = 4 cm
In ΔABO,
OB ⊥ AB (Radius ⊥ tangent at the point of contact)
Applying Pythagoras theorem in ΔABO, we obtain
AB2 + BO2 = OA2
42 + BO2 = 52
16 + BO2 = 25
BO2 = 25-16
BO2 = 9
BO = 3
Hence, the radius of the circle is 3 cm.