Question

[PT = length of tangent, $(x_1,y_1)$ is the point where the tangent is drawn, is the angle the tangent makes with x-axis, $x_1,y_1$, PT > 0]

How many of the following gives the length of subtangent ?

• A. $\frac{y_1}{tan\theta }$
• B. PT cos $\theta$
• C. $\frac{y_1}{cot\theta }$
• D. PT sin $\theta$

Answer 1

Answer: (A), (B)

PT cos $\theta$

The coordinates of P is given as $(x_1,y_1)$ 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($\theta$) = $\frac{P{P}_1}{P_{1}T}$

=> P₁T = PP1 tan($\theta$)= y1 tan($\theta$)

=> A is correct

From the same triangle, we can write cos ($\theta$) = $\frac{P_{1}T}{PT}$

=> P₁T = PT cos $\theta$

=> B is also correct

=> Both of them are correct