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Standard X

Mathematics

Construction of Tangent When Point is on the Circle

In the figure...

Question

In the figure is a tangent to a circle. and are two points on

the circle. If BTP = $72^{0}$ and ATB = $43^{0}$ find ABT.

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Solution

BTP = ABT = $72^{0}$ (The angle between a tangent & chord through the point of contact is equal to an angle in the alternate segment)

In $Δ$ ABT, ABT = $(180^{0} - 72^{0} - 43^{0})$ = $65^{0}$ (Sum of all angles of triangle is $180^{0}$ )

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In the figure is a tangent to a circle. and are two points on the circle. If BTP = 720 and ATB = 430 find ABT.

BTP = ABT = 720 (The angle between a tangent & chord through the point of contact is equal to an angle in the alternate segment) In Δ ABT, ABT = (1800−720−430) = 650 (Sum of all angles of triangle is 1800)

In the figure is a tangent to a circle. and are two points on

the circle. If BTP = $72^{0}$ and ATB = $43^{0}$ find ABT.

BTP = ABT = $72^{0}$ (The angle between a tangent & chord through the point of contact is equal to an angle in the alternate segment)

In $Δ$ ABT, ABT = $(180^{0} - 72^{0} - 43^{0})$ = $65^{0}$ (Sum of all angles of triangle is $180^{0}$ )