Question

Which of the following gives the length of subtangent ?

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

• A.
• B. PT cos θ

Answer 1

Answer: (A), (B)

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 $tan\left(\theta \right)=\frac{PP₁}{P₁T}$ $\Rightarrow P₁T=PP₁tan\left(\theta \right)=y1/tan\left(\theta \right)$ $\Rightarrow$ A is correct From the same triangle, we can write $cos\left(\theta \right)=\frac{P₁T}{PT}$ $\Rightarrow P₁T=PTcos\theta$ $\Rightarrow$ B is also correct $\Rightarrow$ Both of them are correct