Mathematics 10 — Exercise Review · Q3

Full question

A chord 6 cm long is at perpendicular distance 4 cm from the centre of a circle. Find the radius.

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.

   $$\mathrm{MB}=\frac{6}{2}$$

4. Calculate the half-chord length.

   $$\mathrm{MB}=3$$

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

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

6. Calculate this operation before combining the remaining terms.

   $$4^2=16$$

7. Calculate this operation before combining the remaining terms.

   $$3^2=9$$

8. Calculate this operation before combining the remaining terms.

   $$16+9=25$$

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.