If `H` is the othrocenter of an acute angled triangle ABC whose circumcircle is `x^2+y^2=16 ,` then circumdiameter of the triangle HBC is 1 (b) 2 (c) 4 (d) 8

Explanation

To solve the problem, we need to find the circumdiameter of triangle HBC, where H is the orthocenter of triangle ABC, and the circumcircle of triangle ABC is given by the equation \(x^2 + y^2 = 16\).

### Step-by-Step Solution:

1. **Identify the circumradius of triangle ABC**:
The equation of the circumcircle is given as \(x^2 + y^2 = 16\). This can be rewritten in the standard form of a circle, where the radius \(R\) is given by:
\[
R = \sqrt{16} = 4
...