Constructions — Karnataka (SSLC) Class 10 Mathematics Solutions (Free)
Free step-by-step Karnataka (SSLC) Class 10 Mathematics solutions for "Constructions" — important questions with detailed answers, download PDF for board exam preparation.
TL;DR: Free step-by-step Karnataka (SSLC) Class 10 Mathematics solutions for "Constructions" — important questions with detailed answers, download PDF for bo…
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Q1: Draw a tangent to a circle of radius 3 cm at a point on the circumference using compass and straightedge. State the steps clearly.
Step 1: Draw a circle with centre O and radius 3 cm using compass.
Step 2: Mark a point P on the circumference of the circle.
Step 3: Draw the radius OP using a straightedge.
Step 4: Place compass at P and draw two arcs on either side of OP at equal distance from O, creating points A and B on OP extended.
Step 5: The tangent at P is the line perpendicular to OP passing through P. Use compass to construct this perpendicular: place compass at P with radius greater than the distance to O, draw two …
Q2: Divide a line segment AB of length 6 cm in the ratio 3:2 internally.
Step 1: Draw line segment AB = 6 cm using straightedge and compass.
Step 2: Draw an acute angle at A, making any angle with AB. Call this ray AX.
Step 3: On ray AX, mark 5 points (since ratio is 3:2, total parts = 3 + 2 = 5) at equal distance using compass. Name these points A₁, A₂, A₃, A₄, A₅ such that AA₁ = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅.
Step 4: Join A₅B using straightedge.
Step 5: Through point A₃ (which is 3 parts from A), draw a line parallel to A₅B. Use compass and straightedge to construct th…
Q3: Construct a triangle with sides 5 cm, 6 cm, and 7 cm. Then construct a tangent to the circumcircle at any vertex.
Step 1: Draw base BC = 6 cm using straightedge and compass.
Step 2: From B, set compass to 5 cm radius and draw an arc above BC.
Step 3: From C, set compass to 7 cm radius and draw an arc above BC intersecting the first arc at point A.
Step 4: Join AB and AC to complete triangle ABC with sides AB = 5 cm, BC = 6 cm, AC = 7 cm.
Step 5: Construct the circumcircle of triangle ABC by finding the circumcentre (intersection of perpendicular bisectors of two sides). Draw perpendicular bisectors of AB an…
Q4: Draw two tangents to a circle of radius 2.5 cm from an external point P which is 5 cm away from the centre O.
Step 1: Draw a circle with centre O and radius 2.5 cm.
Step 2: Mark point P at distance 5 cm from O (OP = 5 cm).
Step 3: Join O and P using straightedge.
Step 4: Find the midpoint M of OP by constructing perpendicular bisector of OP using compass.
Step 5: Draw a circle with centre M and radius MO (= MF = 2.5 cm).
Step 6: This circle intersects the original circle at two points, say T₁ and T₂. These are the points of contact of tangents from P.
Step 7: Join PT₁ and PT₂. These are the two required…
Q5: Construct a line segment of length √5 cm using compass and straightedge.
Step 1: We know that 5 = 1² + 2². So we can use Pythagoras theorem to construct √5.
Step 2: Draw a perpendicular to a line at a point. Using compass, construct a right angle.
Step 3: From the vertex of right angle, measure 1 cm on one arm and 2 cm on the other arm using compass.
Step 4: Mark points A and B at these distances from the right angle vertex O.
Step 5: Join AB using straightedge. By Pythagoras theorem, AB = √(1² + 2²) = √5 cm.
Alternatively: Draw a right triangle with legs 1 cm and 2 …
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