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From point Q the length of tangent to circle is 24 cm and the distance Q from the centre is 25 cm then the area of the circle is:A. 7 piB. 14 piC. 49 piD. None of these |
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Answer» LET the point of tangency (The point where the TANGENT and radius meets in a circle) be P and the centre be O. According to question:
We KNOW, the tangent is perpendicular to the radius of the circle at the point of tangency. So, ∆OPQ is a right-angled triangle. By using Pythagoras theoram, ⇛ OP² + PQ² = OQ² ⇛ OP = √OQ² - PQ² ⇛ OP = √25² - 24² ⇛ OP = √49 cm ⇛ OP = 7 cm Radius of the circle is 7 cm. Now we can find the area of the circle by using formula, ⇛ Area = πr² ⇛ Area = 7² × π ⇛ Area = 49π The options are in the form of π, hence the correct answer is Option C. And we are done.... |
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