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

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

Question
Circles
asked 2021-01-25
Point B is a point of tangency. Find the radius r of ☉C.

Answers (1)

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
0

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