Construction Full Video || Chapter – 11 || Class 10th (For Hindi Medium)
Dividing a Line Segment
Bisecting a Line Segment
Step 1: With a radius of more than half the length of the line-segment, draw arcs centred at either end of the line segment so that they intersect on either side of the line segment.
Step 2: Join the points of intersection. The line segment is bisected by the line segment joining the points of intersection.
PQ is the perpendicular bisector of AB
2) Given a line segment AB, divide it in the ratio m:n, where both m and n are positive integers.
Suppose we want to divide AB in the ratio 3:2 (m=3, n=2)
Step 1: Draw any ray AX, making an acute angle with line segment AB.
Step 2: Locate 5 (= m + n) points A1,A2,A3,A4andA5 on AX such that AA1=A1A2=A2A3=A3A4=A4A5
Step 3: Join BA5.(A(m+n)=A5)
Step 4: Through the point A3(m=3), draw a line parallel to BA5 (by making an angle equal to ∠AA5B) at A3 intersecting AB at the point C.
Then, AC : CB = 3 : 2.
Division of a line segment
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Constructing Similar Triangles
Constructing a Similar Triangle with a scale factor
Suppose we want to construct a triangle whose sides are 3/4 times the corresponding sides of a given triangle
Step 1: Draw any ray BX making an acute angle with side BC (on the side opposite to the vertex A).
Step 2: Mark 4 consecutive distances(since the denominator of the required ratio is 4) on BX as shown.
Step 3: Join B4C as shown in the figure.
Step 4: Draw a line through B3 parallel to B4C to intersect BC at C’.
Step 5: Draw a line through C’ parallel to AC to intersect AB at A’. ΔA′BC′ is the required triangle.
The same procedure can be followed when the scale factor > 1.
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Drawing Tangents to a Circle
A tangent to a circle is a line which touches the circle at exactly one point.
For every point on the circle, there is a unique tangent passing through it.
PQ is the tangent, touching the circle at A
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Number of Tangents to a circle from a given point
i) If the point in an interior region of the circle, any line through that point will be a secant. So, in this case, there is no tangent to the circle.
AB is a secant drawn through the point S
ii) When the point lies on the circle, there is accurately only one tangent to a circle.
PQ is the tangent touching the circle at A
iii) When the point lies outside of the circle, there are exactly two tangents to a circle.
PT1 and PT2 are tangents touching the circle at T1 and T2
Drawing tangents to a circle from a point outside the circle
To construct the tangents to a circle from a point outside it.
Consider a circle with centre O and let P be the exterior point from which the tangents to be drawn.
Step 1: Join the PO and bisect it. Let M be the midpoint of PO.
Step 2: Taking M as the centre and MO(or MP) as radius, draw a circle. Let it intersect the given circle at the points Q and R.
Step 3: Join PQ and PR
Step 3:PQ and PR are the required tangents to the circle.
Drawing Tangents to a circle from a point on the circle
To draw a tangent to a circle through a point on it.
Step 1: Draw the radius of the circle through the required point.
Step 2: Draw a line perpendicular to the radius through this point. This will be tangent to the circle.