Question

# In the given figure, if AD, AE and BC are tangents to the circle at D, E and F respectively, Then, (a) AD = AB + BC + CA (b) 2AD = AB + BC + CA (c) 3AD = AB + BC + CA (d) 4AD = AB + BC + CA

Solution

## In the given problem, the Right Hand Side of all the options is same, that is, AB + BC + CA So, we shall find out AB + BC + CA and check which of the options has the Left Hand Side value which we will arrive at. By looking at the figure, we can write, AB + BC + CA = AB + BF + FC + CD We know that tangents drawn from an external point will be equal in length. Therefore, BF = BE FC= CD Now we have, AB + BC + CA = AB + BE + CD + CA AB + BC + CD = (AB + BE) + (CD + CA) By looking at the figure, we write the above equation as, AB + BC + CD = AE + AD Since tangents drawn from an external point will be equal, AE = AD Therefore, AB + BC + CD = AD + AD AB + BC + CD = 2AD Therefore option (b) is the correct answer. MathematicsRD Sharma (2020, 2021)All

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