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:

412=c1(c1+c2) 1624=c2c1  412=c12+1624 c1=4121624=40.212 cm c2=1624/c1=1.592 cm d=c1+c2=41.8 cm41^2=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}



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