Question
A tangent is drawn from an external point P to a circle,
touching the circle at point Q such that PQ = 16cm. A secant PRS is also drawn from P, intersecting the circle at points R and S. Given that PR = 8 cm, determine the length of the chord RS.Solution
We know that,
PQ 2 = PR × PS (Tangent secant theorem)
So, 16 2 = 8 × PS
Or, 256 = 8 × PS
Or, PS = 32 cm
RS = PS – PR
So, RS = 32 – 8 = 24 cm
Therefore, the length of chord is 24 cm.
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