Question : A circle touches all four sides of a quadrilateral ABCD. If AB = 18 cm, BC = 21 cm, and AD = 15 cm, then length CD is:
Option 1: 16 cm
Option 2: 14 cm
Option 3: 12 cm
Option 4: 18 cm
Correct Answer: 18 cm
Solution :
Given: A circle touches all four sides of a quadrilateral ABCD. AB=18 cm, BC=21 cm and AD=15 cm.
We know that the lengths of tangents drawn from an external point are equal.
Using this we get,
AB + CD = AD + BC
So, CD = (AD + BC) – AB
= (15 + 21) – 18
= 36 – 18
= 18 cm
Hence, the correct answer is 18 cm.
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