Each question is followed by two statements, A and B. Choose the option based on the given statements and questions

Question 158

There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external point D at a distance d cm from the centre. What are the angles between each tangent and the X-axis?

A.The coordinates of D are given

B.The X-axis bisects one of the tangents.


From statement I, We can draw the following figure

From the figure we can say that in triangle GCD we know 2 sides GC and CD, so we can find the third side
Also we can find the angle GDC(Using trigonometric ratios)

Similarly in triangle CDE, we know CE and DE, so we can find angle CDE.
From this we can get the angle FDE. Now in right angled triangle FDE, we can find the angle DFE.
So we can answer from statement I
Now let us consider statement II

By using trigonometric relations angle CFG can be calculated.
From this we can get angle DFE
Iin triangle CGD we can find angles GDC(Using trigonometric ratios)
Thus we can find EDH and from that we can find EHD.
Hence the question can be answered from statement II alone.

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