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KENDRIYA   VIDYALAYA NEPANAGAR
MATHS PROJECT WORK
MADE BY:   1).AKSHAY FEGADE 2).ABHAY RAJPAL 3).ABHIJEET SINGH TOMAR 4).ANKIT MISHRA
Circles
10.1 Tangents to Circles
INDEX Objectives/Assignment ,[object Object],[object Object],[object Object],[object Object],[object Object]
Some definitions you need ,[object Object],[object Object]
Some definitions you need ,[object Object],[object Object]
Some definitions you need ,[object Object],[object Object]
Some definitions you need ,[object Object],[object Object]
Some definitions you need ,[object Object],[object Object]
Ex. 1:  Identifying Special Segments and Lines ,[object Object],[object Object],[object Object],[object Object],[object Object]
Ex. 1:  Identifying Special Segments and Lines ,[object Object],[object Object],[object Object],[object Object],[object Object]
Ex. 1:  Identifying Special Segments and Lines ,[object Object],[object Object],[object Object]
Ex. 1:  Identifying Special Segments and Lines Tell whether the line or segment is best described as a chord, a secant, a tangent, a diameter, or a radius of  C. c.  EG – a tangent because it intersects the circle in one point.
Ex. 1:  Identifying Special Segments and Lines ,[object Object],[object Object],[object Object]
More information you need-- ,[object Object],2 points of intersection.
Tangent circles ,[object Object],Internally tangent Externally tangent
Concentric circles ,[object Object],Concentric circles No points of intersection
Ex. 2:  Identifying common tangents ,[object Object]
Ex. 2:  Identifying common tangents ,[object Object],[object Object]
Ex. 2:  Identifying common tangents ,[object Object],[object Object],In a plane, the  interior of a circle  consists of the points that are  inside  the circle.  The  exterior of a circle  consists of the points that are  outside  the circle.
Ex. 3:  Circles in Coordinate Geometry ,[object Object]
Ex. 3:  Circles in Coordinate Geometry ,[object Object]
Using properties of tangents ,[object Object]
Theorem 10.1 ,[object Object],[object Object],l
Theorem 10.2 ,[object Object],[object Object],l
Ex. 4:  Verifying a Tangent to a Circle ,[object Object],[object Object]
Ex. 5:  Finding the radius of a circle ,[object Object],[object Object]
Solution: (r + 8) 2  = r 2  + 16 2 Pythagorean Thm. Substitute values c 2  = a 2  + b 2 r  2  + 16r + 64 = r 2  + 256 Square of binomial 16r + 64 = 256 16r = 192 r = 12 Subtract r 2  from each side. Subtract 64 from each side. Divide. The radius of the silo is 12 feet.
Note: ,[object Object]
Theorem 10.3 ,[object Object],[object Object]
Proof of Theorem 10.3 ,[object Object],[object Object],[object Object]
Proof ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Ex. 7:  Using properties of tangents ,[object Object],[object Object],[object Object],x 2  + 2
Solution: x 2  + 2 11 = x 2  + 2 Two tangent segments from the same point are   Substitute values AB = AD 9 = x 2 Subtract 2 from each side. 3 = x Find the square root of 9. The value of x is 3 or -3.
THANK YOU!!!

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Cbse 10th circles

  • 1. KENDRIYA VIDYALAYA NEPANAGAR
  • 3. MADE BY: 1).AKSHAY FEGADE 2).ABHAY RAJPAL 3).ABHIJEET SINGH TOMAR 4).ANKIT MISHRA
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15. Ex. 1: Identifying Special Segments and Lines Tell whether the line or segment is best described as a chord, a secant, a tangent, a diameter, or a radius of C. c. EG – a tangent because it intersects the circle in one point.
  • 16.
  • 17.
  • 18.
  • 19.
  • 20.
  • 21.
  • 22.
  • 23.
  • 24.
  • 25.
  • 26.
  • 27.
  • 28.
  • 29.
  • 30. Solution: (r + 8) 2 = r 2 + 16 2 Pythagorean Thm. Substitute values c 2 = a 2 + b 2 r 2 + 16r + 64 = r 2 + 256 Square of binomial 16r + 64 = 256 16r = 192 r = 12 Subtract r 2 from each side. Subtract 64 from each side. Divide. The radius of the silo is 12 feet.
  • 31.
  • 32.
  • 33.
  • 34.
  • 35.
  • 36. Solution: x 2 + 2 11 = x 2 + 2 Two tangent segments from the same point are  Substitute values AB = AD 9 = x 2 Subtract 2 from each side. 3 = x Find the square root of 9. The value of x is 3 or -3.