IEO Level 2- English Olympiad (SOF) Class 9 Coaching Programs

⏳ 🎯 Online Tests (2 Tests [50 Questions Each]): NTA Pattern, Analytics & Explanations

Click Here to View & Get Complete Material

Rs. 200.00

3 Year Validity (Multiple Devices)

🎓 Study Material (303 Notes): 2024-2025 Syllabus

Click Here to View & Get Complete Material

Rs. 450.00

3 Year Validity (Multiple Devices)

🎯 250 MCQs (& PYQs) with Full Explanations (2024-2025 Exam)

Click Here to View & Get Complete Material

Rs. 200.00

3 Year Validity (Multiple Devices)

Math՚s: Division of a Line Segment: Construction of Similar Triangles and Tangents

Construction of Similar Triangles

Similar Triangle

Illustration: 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 .

Illustration: Similar Triangle with a Given 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

Illustration: 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

Illustration: Construction of Tangents to a Circle
  • 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.