Math, asked by nadim2237, 8 months ago

The lion joining point (0, 5) and (4, 1) is a tangent to a circle whose centre C is at the point (4, 4) find the coordinate of the point of contact of tangent line AB with the circle

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Answered by manevarsha08
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Circles

Tangent to a Circle

The line 2x- y + 1 =0 is ...

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Asked on January 17, 2020 by

Nivetha Kalra

The line 2x−y+1=0 is tangent to the circle at the point (2,5) and the centre of the circles lies on x−2y=4. The radius of the circle is

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Given:

Tangent, T:2x−y+1=0

Slope of tangent, T to the circle is 2

The line joining the centre and the point of contact of tangent is perpendicular with the tangent.

Thus, slope of line OA=−

2

1

Equation of OA,

(y−5)=−

2

1

(x−2)

x+2y=12

∴ Intersection with x−2y=4 will give coordinates of centre which are (8,2)

∴r=OA=

(8−2)

2

+(2−5)

2

=3

5

Hence, option A.

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Answered by nagathegenius
1

Answer:

Step-by-step explanation:

slope of line joining points = -1

therefore equation of tangent = x+y=5

slope of normal = 1

therefore equation of normal = x-y=0

point of intersection of normal and tangent gives point of contact

therefore point of contact = (5/2,5/2)

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