# Point B is a point of tangency. Find the radius r of ☉C.

Question
Circles
Point B is a point of tangency. Find the radius r of ☉C.

2021-01-26
Since point B is a point of tangency, then $$\displaystyle{A}{B}¯¯¯¯¯≅{B}{C}¯¯¯¯¯$$. Hence, $$\displaystyle∠{B}$$ is a right angle and $$\displaystyle△{A}{B}{C}$$ is a right triangle. Using Pythagorean Theorem,
$$\displaystyle{A}{B}^{{2}}+{B}{C}^{{2}}={A}{C}^{{2}}$$
$$\displaystyle{14}^{{2}}+{r}^{{2}}={\left({r}+{7}\right)}^{{2}}$$
$$\displaystyle{196}+{r}^{{2}}={r}^{{2}}+{14}{r}+{49}$$
196=14r+49
147=14r
10.5=r
or
r=10.5

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