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In a circle of unit radius, a tangent PT is drawn from an external point T. If the angle TOP between the radius OP at the contact and the line OT to the external point equals x, the tangent length PT equals:
Answer & Solution
Correct answer: B.
1. Triangle OPT is right-angled at P with right angle between OP and PT.
2. OP equals 1 (unit radius) and angle TOP equals x.
3. From the right triangle, tan x equals opposite (PT) divided by adjacent (OP) = PT divided by 1.
4. Therefore PT equals tan x.
5. This is the geometric origin of the name 'tangent' for the trigonometric ratio.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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