Question

5.2 Two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm.

Answer 1

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of the smaller chord AB is 4 cm.

What are Similar Figures?

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

The diagram for the given condition can be drawn as shown below. Therefore, the measure of the smaller chord AB can be found as shown below.

The two triangles, ΔOPQ and ΔOAB are similar. Therefore, for similar triangles, we can write,

$\dfrac{PQ}{AB} = \dfrac{OQ}{OB}=\dfrac{PO}{AO}$

Now, we can write further,

$\dfrac{13}{AB} = \dfrac{7}{4}$

AB = 7.43 cm

Hence, the length of the smaller chord AB is 4 cm.

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