Question

The angle between the tangents drawn from the origin to the circle \((x-7)^2+(y+1)^2 = 25\) is

• A. \(45^{\circ}\)
• B. \(90^{\circ}\)
• C. \(60^{\circ}\)
• D. \(30^{\circ}\)

Hint:

Use sin(half angle) = radius / distance of the point from the centre.

Answer 1

The Correct Option is B

Step 1: Check position
Centre $(7,-1)$, $r = 5$; $d = \sqrt{50} > 5$, so the origin is outside.

Step 2: Right triangle
Tangent length $L = \sqrt{d^2 - r^2} = \sqrt{50 - 25} = 5$.

Step 3: Angle
$\tan\alpha = r/L = 1$, so $\alpha = 45^{\circ}$ and the full angle is $90^{\circ}$. Option (B).

Final Answer:
Option (B). \[ \boxed{90^{\circ}} \]