PN is a secant intersecting a circle at points M and N such that PN > PM. A tangent PT is drawn to the circle touching it at T. If PM = 32 cm and PT = 40 cm, what is the length (in cm) of the chord MN?

Correct option is D

A tangent PT is  the circle touching it at T.

Concept Used:

$$PT^2 = PM \times PN$$ 

Solution:

​$$PT = 40cm$$ 

$$PM = 32 cm$$ 

$$40^2 = 32 \times PN$$ 

$$1600 = 32 \times PN$$ 

​$$PN = \frac{1600}{32} = 50cm$$ ​

PN=PM+MNPN = PM + MN $$PN = PM + MN$$ 

$50=32+MN$

$MN=50-32$

$MN=18$

$MN$​