Question

to draw a tangent of length 8 cm to a circle of radius 6cm point p should be at a distance of________from the center.

Answer 1

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Given that,

Radius of circle (OA) = 8cm

Chord (AB) = 12cm

Draw OC⊥AB

We know that

The perpendicular from center to chord bisects the chord

∴AC= BC = 12/2 = 6cm

Now in Triangle OCA, by Pythagoras theorem

AC*AC + OC*OC = OA*OA

=>62 + OC*OC = 82

=>36 + OC*OC = 64

=>OC*OC = 64-36

=> OC*OC = 28

=>OC = 28−−√ 28

=>OC = 5.291cm