Q. 33.7( 19 Votes )

If the tangent at a point P to a circle with centre O cuts a line through O at Q such that PQ = 24 cm and OQ = 25 cm. Find the radius of the circle.

Answer :

Given: PQ = 24 cm


OQ = 25 cm


To find: The value of OT.


Theorem Used:


1.) A tangent to a circle is perpendicular to the radius through the point of contact.


2.) Pythagoras theorem:


In a right-angled triangle, the squares of the hypotenuse is equal to the sum of the squares of the other two sides.


Explanation:


Since QT is a tangent to the circle at T and OT is radius,


Therefore, by the theorem stated, OT perpendicular QT


In ΔOTQ,


By Pythagoras theorem we have



OQ2 = OT2 + TQ2


For the given values,



OT2 = 252 – 242


OT2 = 625 – 576


OT2 = 49


OT = √49


OT=7 cm


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