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प्रश्न
Ruler and compasses only may be used in this question. All constructions lines and arcs must be clearly shown, and the be sufficient length and clarity to permit assessment:
(i) Construct a triangle ABC, in which AB = 9 cm, BC = 10 cm and angle ABC = 45°.
(ii) Draw a circle, with center A and radius 2.5 cm. Let it meet AB at D.
(iii) Construct a circle to touch the circle with center A externally at D and also to touch the line BC.
उत्तर
Steps of construction:
1) Take BC = 10 cm
2) Make ∠ ABC = 45° and with centre B, cut the arc = 9 cm.
3) Join AC, So Δ ABC is the required triangle.
4) With A as centre and radius = 2.5 cm, draw a circle. It will pass through D.
5) Draw DE ⊥ AB, which cuts BC at E.
6) Draw the angle bisector of ∠ BED which cut BD at O.
7) Taking Radius = OD to draw a circle which touches the first circle at D and also touches the line BC at F.
8) This is the required circle. The radius OD = 2.7 cm.
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संबंधित प्रश्न
Using a ruler and a compass, construct a triangle ABC in which AB = 7 cm, ∠CAB = 60° and AC = 5 cm. Construct the locus of :
- points equidistant from AB and AC.
- points equidistant from BA and BC.
Hence construct a circle touching the three sides of the triangle internally.
Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them.
Construct a triangle ABC in which base BC = 6 cm, AB = 5.5 cm and ∠ABC = 120°.
Construct a circle circumscribing the triangle ABC.
Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.
Using ruler and compasses only,
- Construct triangle ABC, having given BC = 7 cm, AB – AC = 1 cm and ∠ABC = 45°.
- Inscribe a circle in the ΔABC constructed in (i) above. Measure its radius.
Using a ruler and compasses only:
- Construct a triangle ABC with the following data: AB = 3.5 cm, BC = 6 cm and ∠ABC = 120°.
- In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
- Measure ∠BCP.
Using ruler and compasses only, construct Δ ABC in which BC=7.5 cm, ∠ ABC = 60° and AC - AB= 1.5 cm. Inscribe a circle in the Δ ABC and measure its radius.
Perpendicular bisectors of the sides AB and AC of a triangle ABC meet at O.
Does the perpendicular bisector of BC pass through O?
Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.
Use ruler and compasses only for this question:
(i) Construct A ABC, where AB = 3.5 cm, BC = 6 cm and ∠ ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC, and also equidistant from B and C. Measure and record the length of PB.
(i) Construct a triangle ABC, in which AB = 5.0 cm, BC = 3.5 cm and ∠ ABC = `67 1/2°`
( Use a pair of compasses and ruler only.)
(ii) Construct a circle to touch AB at B and it pass though C.
