the four sides of a quadrilateral ABCD are tangential to a circle. If AB =7.2cm
bc= 8.5 cm and DA = 6.9 cm, then CD = ......... cm.
Answers
CD = 8.2 cm
Step-by-step explanation:
The four sides of a quadrilateral ABCD are tangential to a circle.
- The dimension of quadrilateral are,
AB =7.2cm
, BC= 8.5 cm and DA = 6.9 cm
Please see the attachment for figure.
Each side of diagonal touches circle at P, Q, R and S
Tangent from external point: The length of tangent is equal from external point of a circle.
Therefore,
- AP = AS = a
- BP = BQ = b
- CQ = CR = c
- DR = DS = d
AB = 7.2
AP + BP = 7.2
a + b = 7.2 --------------- (1)
BC = 8.5
BQ + QC = 8.5
b + c = 8.5 ---------------(2)
CR + DR = CD
c + d = CD (Need to find)
AD = 6.9
AS + DS = 6.9
a + d = 6.9 ----------------(3)
Subtract eq(2) - eq(1)
c - a = 1.3 --------------- (4)
Add eq(3) and eq(4)
c + d = 6.9 + 1.3
c + d = 8.2
CD = 8.2 cm
Hence, the length of side of CD is 8.2 cm
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Step-by-step explanation:
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