Question

student-name Hamda Azmi asked in Math
Two cocentric circles with centre O hav A, B, C and D as point of intersection with a line l. If AD = 12 cm and BC = 8cm , find the length of AB and CD and AC

Answer 1

given,

AD = 12 cm and BC = 8 cm

according to the question,

In small circle, OB = OC (radii)

In big circle, OA = OD

=> AB + BO = OC + CD

=> AB = CD

=> AB = CD = x

we know that,

AD = 12

=> AB + BC + CD = 12

=> x + 8 + x = 12

=> 2x = 4

=> x = 4/2 = 2 cm

AB = CD = 2 cm

AC = AB + BC = 2 + 8 = 10 cm

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Answer 2

Two concentric circles with centre O.
And A,B,C,D are point of intersection with line l.
In smaller circle we have,
radius=radius
OB=OC..........................................1
In bigger circle,
radius = radius
OD=OA..........................................2
we have,
AD=12cm
BC=8cm
By eq2 we have,
OC+CD=OB+AB
By eq1 we get,
OB+CD=OB+AB
CD=AB............................................3
AD=12cm
BC+AB+CD=12
8+2AB=12 (by eq3)
AB=2cm=CD
now,
AC=BC+AB=8+2=10
Hence AB=CD=2cm and AC=10cm