Question

I need help with these questions (see image). Please show workings.​

Answer 1

Answer:

r = $\frac{1}{2}$ $\sqrt{l^2+4h^2}$

Step-by-step explanation:

h bisects l at right angles.

There is a right triangle formed with legs h and $\frac{1}{2}$ l and hypotenuse r

Using Pythagoras' identity, then

r² = ($\frac{1}{2}$ l )² + h²

   = $\frac{1}{4}$ l² + h² ← factor out $\frac{1}{4}$

    = $\frac{1}{4}$ (l² + 4h²)

Take the square root of both sides

r = $\sqrt{\frac{1}{4}(l^2+4h^2) }$ = $\frac{1}{2}$ $\sqrt{l^2+4h^2}$

Answer 2

Answer:

• r = $\sqrt{(l/2)^2 + h^2}$

Step-by-step explanation:

Connect the endpoints of the with the center. The formed triangle is isosceles with sides l, r and r.

The height of the triangle h, is the distance between the center of the circle and the midpoint of the chord.

As per Pythagorean theorem we have:

• (l/2)² + h² = r²
• $\sqrt{(l/2)^2 + h^2}$ = r
• r = $\sqrt{(l/2)^2 + h^2}$