Question
Download Solution PDFIn the following figure, O is the centre of the circle. If OP = 5 cm and radius of the circle is 3 cm, find the length of the tangent PT.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
O is the center of the circle.
OP = 5 cm
Radius of the circle (OT) = 3 cm
PT is a tangent to the circle at point T.
Formula Used:
The radius to the point of tangency is perpendicular to the tangent. Therefore, ∠OTP = 90°.
Pythagorean theorem: In a right-angled triangle, (hypotenuse)2 = (base)2 + (perpendicular)2
In right-angled triangle OTP, OP is the hypotenuse, OT and PT are the other two sides.
Calculation:
In right-angled triangle OTP, by the Pythagorean theorem:
OP2 = OT2 + PT2
52 = 32 + PT2
25 = 9 + PT2
PT2 = 25 - 9
PT2 = 16
PT =
Since length cannot be negative, PT = 4 cm.
The length of the tangent PT is 4 cm.
Last updated on Dec 9, 2024
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