Tangent Problems with Pythagorean Theorem

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* - standards :
understand and use properties of chords , tangents , and secants as an application of triangle similarity .


* - content :
in the diagram , B is the point of tangency . find the raduis r if circle C .

destini and chatari.bmp


* - HOW TO SOLVE :
1) pythagorean theorem .
AC^2 = BC^2 + AB^2

2) substitue .
(r + 50)^2 = r^2 + 70^2

3) multiply .
r^2 + 100r + 2500 = r^2 + 4900

4) subtract r^2 and 2500 from both sides .
100r = 2400

5) divide all sides by 100 .
r = 24 ft

* THE RADIUS OF CIRCLE C IS 24 FT .