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Question

Which of the following gives the length of subtangent ?

[PT = length of tangent, (x1,y1) is the point where the tangent is drawn, θ is the angle the tangent makes with x-axis, x1, y1, PT > 0]


A

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B

PT cos θ

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Solution

The correct options are
A


B

PT cos θ


The coordinates of P is given as (x1, y1) in the question. Y coordinate and PP₁ are same as you can see from the figure. We already saw that P₁T is the length of the subtangent.

In the right angled triangle PTP1, we have tan(θ)=PPPT PT=PPtan(θ)=y1/tan(θ) A is correct From the same triangle, we can write cos(θ)=PTPT PT=PTcosθ B is also correct Both of them are correct


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