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Math՚s: Division of a Line Segment: Construction of Similar Triangles and Tangents
Construction of Similar Triangles
Similar Triangle
To construct a triangle similar to a given triangle with its sides equal to of the corresponding sides of the triangle , follow the given steps-
- Step 1: Let ABC be the given triangle. Draw any ray making an acute angle with BC on the side opposite to vertex .
- Step 2: Locate 5 points so that .
- Step 3: Join and draw a line through parallel to to meet at .
- Step 4: Draw a line though parallel to to meet in
Then is the required Triangle.
Similar Triangle with a Given Scale Factor
Construct a triangle with sides and . Construct another triangle similar to this triangle with scale factor .
- Step 1: Draw of a line segment
- Step 2: Through draw an arc of radius . Through draw another arc of radius to intersect the first arc at A.
- Step 3: Join and to get . B
- Step 4: Draw a ray making an acute angle wit h .
- Step 5: Locate points and on such that
- Step 6: Join and through draw a line parallel to to meet in ′.
Through , draw a line parallel to to meet at .
Then is the required triangle.
Construction of Tangents to a Circle
To draw a tangent to a given circle at a given point on it using the center of the circle, follow the given steps-
- Step 1: Suppose be the given circle with centre and a point on it. Join .
- Step 2: At , draw .
- Step 3: Produce to
Then TPQ is the required tangent.
To draw tangents to a circle from a given point outside it, follow the steps given below
- Step 1: Suppose be the given circle with centre and a point outside it Join .
- Step 2: Draw the right bisector of . Let be mid-point of .
- Step 3: With as centre and radius equal to , draw a circle intersecting the given circle at and .
- Step 4: Join and
Then AP and AQ are the two required tangents.