Mathematics 10 — Exercise 8.1 · Q6

Full question

A chord of a circle is 8 cm long and its perpendicular distance from the centre is 3 cm. Find the radius of the circle.

Step-by-step solution

1. Draw the perpendicular from the centre O to the chord AB, meeting at M.

2. A perpendicular from the centre bisects a chord, so AM=MB=AB/2.

3. Divide the full chord length by 2.

   $$\mathrm{MB}=\frac{8}{2}$$

4. Calculate the half-chord length.

   $$\mathrm{MB}=4$$

5. In right triangle OMB the radius is the hypotenuse: r²=OM²+MB².

   $$r=\sqrt{3^2+4^2}$$

6. Calculate this operation before combining the remaining terms.

   $$3^2=9$$

7. Calculate this operation before combining the remaining terms.

   $$4^2=16$$

8. Calculate this operation before combining the remaining terms.

   $$9+16=25$$

9. Calculate this operation before combining the remaining terms.

   $$\sqrt{25}=5$$

10. Use the positive value because lengths and distances are nonnegative.

    $$5$$

Answer

The final answer is shown below.