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प्रश्न
Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.
- Construct a ΔABC in which BC = 6.5 cm, ∠ABC = 60°, AB = 5 cm.
- Construct the locus of points at a distance of 3.5 cm from A.
- Construct the locus of points equidistant from AC and BC.
- Mark 2 points X and Y which are at a distance of 3.5 cm from A and also equidistant from AC and BC. Measure XY.
उत्तर
- Steps of construction:
- Draw BC = 6.5 cm using a ruler.
- With B as center and radius equal to approximately half of BC, draw an arc that cuts the segment BC at Q.
- With Q as center and same radius, cut the previous arc at P.
- Join BP and extend it.
- With B as center and radius 5 cm, draw an arc that cuts the arm PB to obtain point A.
- Join AC to obtain ΔABC.
- With A as center and radius 3.5 cm, draw a circle.
The circumference of a circle is the required locus.
- Draw CH, which is bisector of ΔACB. CH is the required locus.
- Circle with center A and line CH meet at points X and Y as shown in the figure. xy = 5 cm (approximately).
APPEARS IN
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.
Use graph paper for this question. Take 2 cm = 1 unit on both the axes.
- Plot the points A(1, 1), B(5, 3) and C(2, 7).
- Construct the locus of points equidistant from A and B.
- Construct the locus of points equidistant from AB and AC.
- Locate the point P such that PA = PB and P is equidistant from AB and AC.
- Measure and record the length PA in cm.
Draw and describe the lorus in the following cases:
The locus of points at a distance of 4 cm from a fixed line.
Draw and describe the lorus in the following cases:
The lorus of points inside a circle and equidistant from two fixed points on the circle .
Describe completely the locus of points in the following cases:
Centre of a cirde of radius 2 cm and touching a fixed circle of radius 3 cm with centre O.
Construct a triangle ABC, such that AB= 6 cm, BC= 7.3 cm and CA= 5.2 cm. Locate a point which is equidistant from A, B and C.
Without using set squares or protractor construct a triangle ABC in which AB = 4 cm, BC = 5 cm and ∠ABC = 120°.
(i) Locate the point P such that ∠BAp = 90° and BP = CP.
(ii) Measure the length of BP.
Using ruler and compasses construct:
(i) a triangle ABC in which AB = 5.5 cm, BC = 3.4 cm and CA = 4.9 cm.
(ii) the locus of point equidistant from A and C.
(iii) a circle touching AB at A and passing through C.
Using only a ruler and compass construct ∠ABC = 120°, where AB = BC = 5 cm.
(i) Mark two points D and E which satisfy the condition that they are equidistant from both ABA and BC.
(ii) In the above figure, join AD, DC, AE and EC. Describe the figures:
(a) AECB, (b) ABD, (c) ABE.
How will you find a point equidistant from three given points A, B, C which are not in the same straight line?
