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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10th
Maths
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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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)