Geometric Constructions — Maharashtra (SSC) Class 10 Mathematics Solutions (Free)

Given: Circle with center O and external point P. To construct: Tangent from P to the circle. Steps: Step 1: Join O and P. Step 2: Find midpoint M of OP. Using compass, measure distance OP, place compass at O and P alternately above and below OP line, mark two points, draw line through them to locate M. Step 3: With M as center and MO (or MP) as radius, draw a circle. Step 4: This circle intersects the original circle at two points; let them be A and B. Step 5: Join PA and PB. Both PA and PB are…

Given: Triangle ABC, scale factor k = 3/2. To construct: Triangle similar to ABC with sides 3/2 times larger. Steps: Step 1: Draw triangle ABC. Step 2: Extend AB to a point D such that AD = (3/2) * AB. Alternatively, divide AB into 2 parts, take 3 such parts on extension of AB. Step 3: From B, construct angle equal to angle ABC at D. Step 4: Extend line from D at angle DBA = angle ABC until it meets with line from A parallel to BC at point E. Step 5: Similarly, extend AC to F such that AF = (3/2…

Given: Circle with center O and radius 3 cm, line l. To construct: Tangent to circle parallel to line l. Steps: Step 1: Draw circle with center O and radius 3 cm. Step 2: Draw the given line l. Step 3: From O, draw a perpendicular to line l. Let the foot of perpendicular be H. Step 4: On the perpendicular OH, mark points A and B on opposite sides of O such that OA = OB = 3 cm (the radius). Step 5: Through A and B, draw lines parallel to l. These are the required tangents to the circle parallel t…

Given: Side length 5 cm, scale factor 2/3. To construct: Similar triangle with sides 2/3 times original. Steps: Step 1: Construct equilateral triangle ABC with side 5 cm using compass and ruler. Step 2: To construct similar triangle with scale factor 2/3, sides should be (2/3) * 5 = 10/3 cm (approximately 3.33 cm). Step 3: On side AB, mark point P such that AP = (2/3) * AB. Divide AB into 3 equal parts using parallel lines method, take 2 parts. Step 4: Similarly, on side AC, mark point Q such th…

Given: Line segment AB = 8 cm, ratio 3:5. To divide: Point P on AB such that AP:PB = 3:5. Steps: Step 1: Draw line segment AB of length 8 cm. Step 2: From A, draw a ray AC making acute angle with AB. Step 3: On ray AC, starting from A, mark 3 + 5 = 8 equal segments using compass. Name the points as A1, A2, A3, ..., A8. Step 4: Join A8 to B. Step 5: Through point A3, draw a line parallel to A8B. This parallel line intersects AB at point P. Step 6: By basic proportionality theorem, AP/PB = 3/5, so…