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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.
उत्तर
Steps of construction:
- Draw a line AB = 7 cm.
- Taking P ascentre and same radius, draw an arc of a circle which intersects AB at M.
- Taking M ascentre and with the same radius as before drawn an arc intersecting previously drawn arc, at point N.
- Draw the ray AX passing through N, then
- Taking A ascentre and radius equal to 5 cm, draw an arc cutting AX at C.
- Join BC.
- The required triangle ABC is obtained.
- Draw angle bisector of∠CAB and ∠ABC.
- Mark their intersection as O.
- With O as center, draw a circle with radius OD.
- Hence, AY is the locus of points equidistant from AB and AC.
- Hence, BZ is the locus of points equidistant from BA and BC.
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संबंधित प्रश्न
Construct a ΔABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
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 a triangle ABC in which AB=S cm, BC=6 cm and CA=4.5 cm. Construct a circle passing through A, Band c.
Using ruler and compasses only, construct and equilateral triangle with side 4.5 cm. Draw a circumcircle of this triangle and measure its radius.
Draw a circle of radius 4.5 cm. Take a point Pon its circumference. Construct a tangent to the circle at P without using the centre.
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 a triangle ABC, given that the radius of the circumcircle of triangle ABC is 3.5 cm, ∠ BCA = 45° and ∠ BAC = 60°.
Using ruler and compass only, construct a triangle ABC such that AB = 5 cm, ABC = 75°, and the radius of the circumcircle of triangle ABC is 3.5 cm. On the same diagram, construct a circle, touching AB at its middle point and also touching the side AC.
Construct a Δ ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.
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.
