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Quadrilateral ABCD circumscribes a circle with AB = $3 x$ cm, BC = $(2 x + 1)$ cm, CD = 10 cm and DA = 13 cm. Find $x$ .

Class 10Tangent Lengths and IncirclesGeometry

A4
B3
C2
D5

Step-by-Step Solution

AB + CD = BC + DA:

3 x + 10 = 2 x + 1 + 13

, so

x = 4

. Then AB = 12 cm, BC = 9 cm, and 12 + 10 = 9 + 13 = 22 checks.

Answer: A) 4

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