Advertisements
Advertisements
प्रश्न
Ruler and compasses only may be used in this question. All constructions lines and arcs must be clearly shown, and the be sufficient length and clarity to permit assessment:
(i) Construct a triangle ABC, in which AB = 9 cm, BC = 10 cm and angle ABC = 45°.
(ii) Draw a circle, with center A and radius 2.5 cm. Let it meet AB at D.
(iii) Construct a circle to touch the circle with center A externally at D and also to touch the line BC.
उत्तर
Steps of construction:
1) Take BC = 10 cm
2) Make ∠ ABC = 45° and with centre B, cut the arc = 9 cm.
3) Join AC, So Δ ABC is the required triangle.
4) With A as centre and radius = 2.5 cm, draw a circle. It will pass through D.
5) Draw DE ⊥ AB, which cuts BC at E.
6) Draw the angle bisector of ∠ BED which cut BD at O.
7) Taking Radius = OD to draw a circle which touches the first circle at D and also touches the line BC at F.
8) This is the required circle. The radius OD = 2.7 cm.
APPEARS IN
संबंधित 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.
Construct a regular hexagon of side 5 cm. Hence construct all its lines of symmetry and name them.
In the figure given below 'O' is the centre of the circle. If QR = OP and ∠ORP = 20°. Find the value of 'x' giving reasons
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 ruler and compasses only,
- Construct a triangle ABC with the following data :
Base AB = 6 cm, BC = 6.2 cm and ∠CAB = 60°. - In the same diagram, draw a circle which passes through the points A, B and C and mark its center O.
- Draw a perpendicular from O to AB which meets AB in D.
- Prove that : AD = BD.
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 with radius 3 cm and inscribe an equilateral triangle in it.
Draw line segments OA = 4.5 cm, OB = 3.2 cm such that ∠ AOB = 45°. Construct a circle touching OA at A and passing through B.
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.
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.
