# Tangents

To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.

Correct result:

d =  41.8 cm

#### Solution:

$41^2=c_1(c_1+c_2) \ \\ \dfrac{ 16^2}{4}= c_2 c_1 \ \\ \ \\ 41^2=c_1^2 + \dfrac{ 16^2}{4} \ \\ c_1 = \sqrt{ 41^2 - \dfrac{ 16^2}{4} }= 40.212\ cm \ \\ c_2 = \dfrac{ 16^2}{4} / c_1 = 1.592\ cm \ \\ d=c_1+c_2 = 41.8 \ \text{cm}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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