Constructions Class 10 Notes Maths Chapter 11

CBSE Class 10 Maths Notes Chapter 11 Constructions Pdf free download is part of Class 10 Maths Notes for Quick Revision. Here we have given NCERT Class 10 Maths Notes Chapter 11 Constructions. According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

CBSE Class 10 Maths Notes Chapter 11 Constructions

Determining a Point Dividing a given Line Segment, Internally in the given Ratio M : N

Let

Steps of Construction:

• Draw a line segment AB = x cm.
• Make an acute ∠BAX at the end A of AB.
• Use a compass of any radius and mark off arcs. Take (m + n) points A ₁ , A ₂ , … A _m , A _m+1 , …, A _m+n along AX such that AA ₁ = A ₁ A ₂ = … = A _m+n-1 , A _m+n
• Join A _m+n B.
• Passing through A _m , draw a line A _m P || A _m+n B to intersect AB at P. The point P so obtained is the A required point which divides AB internally in the ratio m : n.
  

Construction of a Tangent at a Point on a Circle to the Circle when its Centre is Known

Steps of Construction:

• Draw a circle with centre O of the given radius.
  
• Take a given point P on the circle.
• Join OP.
  
• Construct ∠OPT = 90°.
  
• Produce TP to T’ to get TPT’ as the required tangent.
  

Construction of a Tangent at a Point on a Circle to the Circle when its Centre is not Known

ABC

Construction of a Tangents from an External Point to a Circle when its Centre is Known

Steps of Construction:

• Draw a circle with centre O.
• Join the centre O to the given external point P.
• Draw a right bisector of OP to intersect OP at Q.
• Taking Q as the centre and OQ = PQ as radius, draw a circle to intersect the given circle at T and T’.
• Join PT and PT’ to get the required tangents as PT and PT’.
  

Construction of a Tangents from an External Point to a Circle when its Centre is not Known

be

Construction of a Triangle Similar to a given Triangle as per given Scale Factor \(\frac { m }{ n }\) , m < n.

the

Steps of Construction:

• Construct a triangle ABC by using the given data.
• Make an acute angle ∠BAX, below the base AB.
• Along AX, mark n points A ₁ , A ₂ …, A _n , such that AA ₁ = A ₁ A ₂ = … = A _m-1 A _m = … A _n-1 A _n .
• Join A _n B.
• From A _m , draw A _m B’ parallel to AnB, meeting AB at B’.
• From B’, draw B’C’ parallel to BC, meeting AC at C’.
  Triangle AB’C’ is the required triangle, each of whose sides is \(\frac { m }{ n }\) (m < n) of the corresponding sides of ΔABC.
  

Construction of a Triangle Similar to a given Triangle as per given Scale Factor \(\frac { m }{ n }\) , m > n.

given

Steps of Construction:

• Construct a ΔABC by using the given data.
• Make an acute angle ∠BAX, below the base AB. Extend AB to AY and AC to AZ.
• Along AX, mark m points A ₁ , A ₂ …, A _n , ..A _m , such that AA ₁ = A ₁ A ₂ = A ₂ A ₃ = … = A _n-1 A _n = … = A _m-1 A _m
• Join A _n B.
• From A _m , draw A _m B’ parallel to A _n B, meeting AY produced at B’.
• From B’, draw B’C’ parallel to BC, meeting AZ produced at C’.
• Triangle AB’C’ is the required triangle, each of whose sides is (\(\frac { m }{ n }\)) (m > n) of the corresponding sides of ΔABC.
  

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