A quadrilateral ABCD is inscribed around a circle. If AB=10 cm, BC=12 cm, and the perimeter of the quadrilateral is 40 cm, what is the length of side CD?
Show answer & explanation
Correct answer: B
Explanation
Given:
AB = 10 cm
BC = 12 cm
Perimeter = 40 cm
AD + CD = 40 − (10 + 12) = 18 cm
In a tangential quadrilateral,
AB + CD = BC + AD
10 + CD = 12 + AD
AD = 18 − CD
10 + CD = 12 + (18 − CD)
10 + CD = 30 − CD
2CD = 20
CD = 10 cm