Chord AB of a circle is produced to a point P, and C is a point on the circle such that PC is a tangent to the circle. If PC = 12 cm, and BP = 10 cm, then the length of AB (in cm) is:
Answer & explanation
Correct answer: option 4
Let AB be x cm.
AP = AB + PB = x + 10
\( {PC }^{2 } \) = AP x PB
= \( {12 }^{2 } \) = 10 x (x + 10)
= \(\frac{144}{10}\) = x + 10
= x + 10 = 14.4
= x + 14.4 - 10
= x = 4.4
Therefore, The length of chord AB is 4.4 cm.