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प्रश्न
Use ruler and compasses only for the following questions:
Construct triangle BCP, when CB = 5 cm, BP = 4 cm, ∠PBC = 45°.
Complete the rectangle ABCD such that :
(i) P is equidistant from AB and BC and
(ii) P is equidistant from C and D. Measure and write down the length of AB.
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उत्तर
Given: BC = 5 cm, BP = 4 cm and ∠PBC = 45°
Steps of construction :
1. Constant ΔBCP with BC = 5 cm, BP = 4 cm and ∠PBC = 45°.
2. Draw perpendicular BE and CF and B and C respectively.
3. Draw perpendicular from on CF meeting CF in K.
4. Cut CD from CF, such that CK = KD.
5. Cut BA from BE, such that BA = CD.
6. Join AD.
Hence, ABCD is the required rectangle and AB = 5·7 cm.
संबंधित प्रश्न
Use ruler and compasses only for this question:
I. Construct ABC, where AB = 3.5 cm, BC = 6 cm and ABC = 60o.
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 records the length of PB.
Describe the locus of vertices of all isosceles triangles having a common base.
In Δ PQR, s is a point on PR such that ∠ PQS = ∠ RQS . Prove thats is equidistant from PQ and QR.
In given figure, ABCD is a kite. AB = AD and BC =CD. Prove that the diagona AC is the perpendirular bisector of the diagonal BD.
State and draw the locus of a swimmer maintaining the same distance from a lighthouse.
Construct a Δ ABC, with AB = 6 cm, AC = BC = 9 cm; find a point 4 cm from A and equidistant from B and C.
Using a ruler and compass only:
(i) Construct a triangle ABC with BC = 6 cm, ∠ABC = 120° and AB = 3.5 cm.
(ii) In the above figure, 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.
Without using set squares or a protractor, construct:
- Triangle ABC, in which AB = 5.5 cm, BC = 3.2 cm and CA = 4.8 cm.
- Draw the locus of a point which moves so that it is always 2.5 cm from B.
- Draw the locus of a point which moves so that it is equidistant from the sides BC and CA.
- Mark the point of intersection of the loci with the letter P and measure PC.
Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords, AB and AC, of the circle of length 6 cm and 5 cm respectively.
- Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction.
- Construct the locus of points, inside the circle, that are equidistant from AB and AC.
Without using set squares or protractor.
(i) Construct a ΔABC, given BC = 4 cm, angle B = 75° and CA = 6 cm.
(ii) Find the point P such that PB = PC and P is equidistant from the side BC and BA. Measure AP.
