Mathematics 10 — Exercise 8.1 · Q7

Full question

In the diagram, A is the centre and AB is perpendicular to chord CD at B. If CD = 121 units and BC = 3x units, find x.

Step-by-step solution

1. The diagram shows a perpendicular from centre A to chord CD at B. It bisects CD.

   $$\mathrm{BC}=\frac{121}{2}$$

2. Calculate the half length: 121÷2=60.5.

   $$\frac{121}{2}$$

3. Given BC=3x, set 3x=121/2.

   $$3\times x=\frac{121}{2}$$

4. Equate the corresponding entries.

   $$3\times x=\frac{121}{2}$$

5. Collect the variable terms on the left and constants on the right.

   $$3\times x=\frac{121}{2}+0$$

6. Simplify the constant calculation.

   $$3\times x=\frac{121}{2}$$

7. Divide both sides by the variable coefficient.

   $$x=\frac{121}{6}$$

8. Reduce the fraction.

   $$x=\frac{121}{6}$$

Answer

The final answer is shown below.