Question

Draw a circle of radius 4.5 cm and construct a chord of length 6 cm. Construct tangents and ends of the chord. ​

Answer 1

⚽ Correct Question ⚽$\:$

Draw a circle of radius 4.5 cm and construct a chord of length 6 cm. Construct tangents and ends of the chord.

⚽Steps⚽

> Draw a circle of radius 4.5cm

> Take a point P on the circle and mark chord PQ of length 6cm

> Join P with center O

> Taking vertex P and base OP draw a perpendicular to OP

> The perpendicular XX′ is the required tangent.

⚽ Similar Question to practice:-

> Draw a chord of length 6 cm in a circle of radius 4 cm and shade the major segment.

> Draw a circle with radiuys 3.4 cm. Draw a chord MN of length 5.7 cm in it. Construct tangents at point M and N to the circle

Answer 2

★ Solution :-

How to construct the given figure ::

• Take a scale and measure 4.5 cm. Take this as the radius using compass and draw a circle of 4.5 cm. The centre of the circle is O.

• OR is the radius of circle = 4.5 cm

• Measure and draw a chord of length of 6 cm in the circle. Point this chord as MN. Draw the chord such that it passes through the radius OR.

• MN is the chord of circle = 6 cm

• Take compass and measure 3 cm using scale. From point M draw an arc at 3 cm on the chord MN which is the midpoint of MN. Similarly draw an arc at 3 cm from N on the chord MN. This will be also midpoint of the chord MN. These both arcs drawn should meet at same point. Mark this point as A.

• MA = NA = midpoint of chord MN = 3 cm

• This means that the radius OR of the circle passes through point A and this radius OR is the perpendicular bisector of MN.

• Take a point P which is 4 cm away from the point A. From this point draw a ray PQ to the point M and similarly draw a ray PS to point N.

These are the required tangents to the circle.

• PQ = PS (tangents drawn from an exterior point to a circle are equal in length).

• Tangent PQ meets one end of the chord MN at the point M so it satisfies the condition.

• Tangent PS meets one end of the chord MN at the point N so it satisfies the condition.

• Verify using protractor that if radius is perpendicular to Tangent.

• So PQ and PS are the required tangents.

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★ More to know :-

• Tangent is the line which meets the circle at only one point.

• Secant is the lime which meets the circle at more than one points.

• Circle is the planar figure which has no beginning nor any end point. It is made by joining all the points on the plane from end to end.

• Perpendicular Bisector is the line which is perpendicularly bisecting another line.

• Chord is the line in the circle which divides the circle in major and minor segments.