Mathematics 10 — Exercise 8.1 · Q1

Full question

A circle has radius 13 cm. A chord is at perpendicular distance 5 cm from the centre. Find the length of the chord.

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. Find the HALF chord using MB²=r²−d².

   $$\sqrt{{13}^2-5^2}$$

4. Calculate this operation before combining the remaining terms.

   $${13}^2=169$$

5. Calculate this operation before combining the remaining terms.

   $$5^2=25$$

6. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times 25=-25$$

7. Calculate this operation before combining the remaining terms.

   $$169-25=144$$

8. Calculate this operation before combining the remaining terms.

   $$\sqrt{144}=12$$

9. The complete chord is twice the half-chord.

   $$\mathrm{AB}=2\times 12$$

10. Calculate that multiplication.

    $$24$$

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

    $$24$$

Answer

The final answer is shown below.