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प्रश्न
Take point P and Q and draw a circle passing through them. Draw a tangent AB to the circle without using the centre of the circle.
उत्तर
Analysis:
Centre of the circle passing through P and Q must be equidistant from points P and Q.
∴ It must lie of perpendicular bisector of seg PQ.
Steps of construction:
- Take any two point P, Q and join them.
- Draw a perpendicular bisector of PQ.
- Take any point O on the perpendicular bisector and draw a circle with centre O and radius OP.
- Take any point A on the major arc of the circle and draw ∆PQA.
- By taking P as centre and any convenient distance on compass draw an arc intersecting the arms of ∠QPA in points T and R.
- With A as centre and the same distance in the compass, draw an arc intersecting the chord QA at point S.
- Taking radius equal to TR and S as centre, draw an arc intersecting the previously drawn arc. Name the point of intersection as B.
- Draw line AB. Line AB is the required tangent to the circle.
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संबंधित प्रश्न
Draw a circle of radius 3.5 cm. Take any point K on it. Draw a tangent to the circle at K without using centre of the circle.
Draw a tangent at any point ‘P’ on the circle of radius 3.5 cm and centre O.
Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.
Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.
Draw a circle with centre O and radius 3.5 cm. Take point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.
Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.
Complete the following activity to draw a tangent to a circle at a point on the circle.
Draw a circle of radius 2.2 cm with O as centre.
↓
Take any point P on the circle and draw ray OP.
↓
Draw a perpendicular line to the ray at point P.
↓
Name the perpendilcular line as l
l is the tangent at point P.
Construct tangent to a circle with centre A and radius 3.4 cm at any point P on it.
Draw a circle of radius 4.2 cm, take any point M on it. Draw tangent to the circle from point M
Do the following activity to draw tangents to the circle without using the center of the circle.
- Draw a circle with radius 3.5 cm and take any point C on it.
- Draw chord CB and an inscribed angle CAB.
- With the center A and any convenient radius, draw an arc intersecting the sides of angle BAC in points M and N.
- Using the same radius, draw an arc intersecting the chord CB at point R.
- Taking the radius equal to d(MN) and center R, draw an arc intersecting the arc drawn in the previous step. Let D be the point of intersection of these arcs. Draw line CD. Line CD is the required tangent to the circle.
Draw a circle with center O and radius 3.6 cm. Draw a tangent to the circle from point B at a distance of 7.2 cm from the center of the circle.
Draw a circle with center C and radius 3.2 cm. Draw a tangent to the circle from point P at a distance of 7.5 cm from the center of the circle
Draw a circle of radius 4.2 cm. Draw arc PQ measuring 120°. Draw a tangent to the circle from point P and point Q
Draw a circle with center O and radius 3 cm. Take the point P and the point Q at a distance of 7 cm from the center of the circle on the opposite side of the circle such that their line of intersection passing through the center of the circle Draw a tangent to the circle from the point P and the point Q
Draw a circle with radius 3 cm. Construct a square such that each of its side will touch the circle from outside
Draw any circle with radius greater than 1.8 cm and less than 3 cm. Draw a chord AB 3.6 cm long in this circle. Tangent to the circle passing through A and B without using the center of the circle
Draw a circle of radius 3.2 cm and centre 'O'. Take any point P on it. Draw tangent to the circle through point P using the centre of the circle.
