Question

Study the diagram of circle L, where RS is tangent to circle L at point S.Also, RS = 24, RL = 26, and LS is a radius.What is the length of the radius, r?

Answer 1

From the figure given,

Where RS is perpedicular to the radius LS and L is the centre of the circle,

Given that

`\begin{gathered} RS=24\text{ units} \\ RL=26\text{ units and } \\ LS=r\text{ units} \end{gathered}`

The formula to find the value of r is the Pythagorean theorem, which is given as

`(\text{HYP)}^2=(OPP)^2+(\text{ADJ)}^2`

Where

`\begin{gathered} \text{HYP=RL}=26\text{ units} \\ OPP=RS=24\text{ units} \\ \text{ADJ=LS}=r\text{ units} \end{gathered}`

Substitute the values into the formula of the Pythagorean theorem

`\begin{gathered} (RL)^2=(RS)^2+(LS)^2 \\ 26^2=24^2+r^2 \\ 676=576+r^2 \\ \text{Collect like terms} \\ r^2=676-576 \\ r^2=100 \\ \text{Square root of both sides} \\ \sqrt[]{r^2}=\sqrt[]{100} \\ r=10\text{ units} \end{gathered}`

Hence, the length of radius, r is 10 units