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Question
AB and BC are the tangents to the circle from the points B. D is the centre of the circle. BD = 5 cm and CD = 3 cm. Find the value of AB - BC.
AB and BC are the tangents to the circle from the points B. D is the centre of the circle. BD = 5 cm and CD = 3 cm. Find the value of AB - BC.
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Solution
The correct option is D 0 cm
In the above diagram,
AD = DC = 3 cm (Radius of the circle)
In ΔADB
AD = 3 cm (Radius of the given circle)
DB = 5 cm (Given)
∠DAB=90∘ (The tangent at any point of a circle and the radius through the point are perpendicular to each other)
(AB)2+(AD)2=(BD)2(AB)2+32=52(AB)2=25−9(AB)2=16
AB = 4
AB = BC = 4 (If two tangents are drawn to a circle from an exterior points, the tangents are equal in length)
AB - BC = 4 - 4 = 0 cm
0 cm
In the above diagram,
AD = DC = 3 cm (Radius of the circle)
In ΔADB
AD = 3 cm (Radius of the given circle)
DB = 5 cm (Given)
∠DAB=90∘ (The tangent at any point of a circle and the radius through the point are perpendicular to each other)
(AB)2+(AD)2=(BD)2(AB)2+32=52(AB)2=25−9(AB)2=16
AB = 4
AB = BC = 4 (If two tangents are drawn to a circle from an exterior points, the tangents are equal in length)
AB - BC = 4 - 4 = 0 cm
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