In a circle of radius 7 cm, tangent PT is drawn from a point P such that PT = 24 cm. If O is the centre of the circle then OP =?
Given, A circle with center O and radius, OT = 7 cm and PT = 24 cm
Now, we know that
Tangent at a point on the circle is perpendicular to the radius through the point of contact.
i.e.
OT ⏊ OP
By Pythagoras Theorem in ΔOTP [ i.e. Hypotenuse2 = Base2 + Height2]
(OP)2 = (OT)2 + (PT)2
⇒ (OP)2 = (7)2 + (24)2
⇒ (OP)2 = 49 + 576 = 625
⇒ OP = 25 cm
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