suppose ab is a diameter of circle shown,bc is tangent to the circle.angle bac equal to 30degrees and cd equal to root 3.what is the distance from a to b .please answer it fast
Anyone!!!!!!!!
Answers
Given : ab is a diameter of circle . bc is tangent to the circle , ∠BAC = 30° . CD = √3
To find : distance from a to b ( Diameter length )
Solution:
AB is Diameter
AC intersect circle at D
Hence ΔADB is right angle triangle
∠BAD = ∠BAC = 30°
=> Cos∠BAD = AD/AB
=> Cos 30° = AD/AB
=> AD = ABCos 30°
AC = AD + CD = ABCos 30° + √3
in ΔABC
Cos∠BAC = AB/AC
=> Cos30° = AB / ( (ABCos 30° + √3 )
=> ABCos²30° + √3Cos30° = AB
Cos30° = √3 / 2
=> AB (3/4) + √3 * √3 / 2 = AB
=> 3/2 = AB/4
=> AB = 6
distance from a to b = 6
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