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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.
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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).
संबंधित प्रश्न
Construct a triangle ABC, with AB = 6 cm, AC = BC = 9 cm. Find a point 4 cm from A and equidistant from B and C.
Plot the points A(2, 9), B(–1, 3) and C(6, 3) on graph paper. On the same graph paper draw the locus of point A so that the area of ΔABC remains the same as A moves.
Draw two intersecting lines to include an angle of 30°. Use ruler and compasses to locate points which are equidistant from these Iines and also 2 cm away from their point of intersection. How many such points exist?
Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD.
Construct a rhombus ABCD whose diagonals AC and BD are 8 cm and 6 cm respectively. Find by construction a point P equidistant from AB and AD and also from C and D.
In Δ PQR, s is a point on PR such that ∠ PQS = ∠ RQS . Prove thats is equidistant from PQ and QR.
In Δ PQR, bisectors of ∠ PQR and ∠ PRQ meet at I. Prove that I is equidistant from the three sides of the triangle , and PI bisects ∠ QPR .
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.
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.
Given ∠BAC (Fig), determine the locus of a point which lies in the interior of ∠BAC and equidistant from two lines AB and AC.
