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प्रश्न
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?
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उत्तर १
Draw an angle bisectcr PQ and RS of angles formed by the lines m and n. From centre draw a circle with radius 2 cm, whidi intersect the angle bisectors at a, b, c and d respectively.
Hence, a, b, c and d are the required four points.
उत्तर २
AB and CD are two intersecting lines at an angle of 30°. Their point of intersection is O.
Draw MON and ROS, the bisector of angles between AB and CD. On ON, locate a point P such that OP = 2 cm.
On OR locate a point Q such that OQ = 2 cm.
Since, P and Q are on the angle bisectors of angles between AB and CD, hence each of P and Q is equidistant from AB and CD.
Also, OP = 2 cm
Hence, P and Q are the required points.
संबंधित प्रश्न
Construct a triangle ABC with AB = 5.5 cm, AC = 6 cm and ∠BAC = 105°
Hence:
1) Construct the locus of points equidistant from BA and BC
2) Construct the locus of points equidistant from B and C.
3) Mark the point which satisfies the above two loci as P. Measure and write the length of PC.
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 a point P, so that:
AB2 = AP2 + BP2,
where A and B are two fixed points.
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.
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 .
Describe completely the locus of a point in the following case:
Centre of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with centre O.
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.
How will you find a point equidistant from three given points A, B, C which are not in the same straight line?
