RD Sharma Solutions Class 10 Constructions Exercise 11.3

RD Sharma Class 10 Solutions Chapter 11 Ex 11.3 PDF Free Download

EXERCISE 11.3

  1. Draw a circle of radius 6 cm. From a point 10 cm away from its center, construct a pair of tangents to the circle and measure their lengths.

    Solutions:

    Given:

    To construct a circle of radius 6 cm and a pair of tangents to the circle from a point, say X, 10 cm from its centre.

    To Find:

    The length of the tangents.

    Sample Figure:

    Class 10 maths chapter 11 constructions Ex 11.3-1

    Construction:

    Step 1. Draw a circle of radius 6 cm.

    Step 2. Make a point X at a distance of 10 cm from O, and join OX.

    Step 3. Draw a right bisector of X, intersecting OX at an angle of 90o at Q.

    Step 4. Draw a circle to intersect the given circle at T and T`, taking Q as center and radius OQ = XQ.

    Step 5. Join XT and X`T` to get the required tangents.

    Hence, XT and X`T` are the tangents.

    Class 10 maths chapter 11 constructions Ex 11.3-2

    To find the length of the tangent, we know that OT⊥PT and ΔOPT is the right triangle.

    Then,

    Since, OT = 6 cm and PO = 10 cm.

    From ΔOPT,

    PT2 =OP2–OT2=(10)2–(6)2 [Using Pythagoras Theorem]

    = 100 – 36

    = 64

    PT = 8 cm

    ∴, length of tangents = 8 cm.

  2. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters each at a distance of 7 cm from its center. Draw tangents to the circle from these points P and Q.

    Solutions:

    Given:

    To construct a circle of radius 3 cm and a tangents to the circle from the points P and Q, where P and Q are two points on one of the extended diameters of the circle, each at a distance of 7 cm from the center of the circle.

    Sample Figure:

    Class 10 maths chapter 11 constructions Ex 11.3-3

    Construction:

    Step 1. First, draw a line segment PQ of 14 cm.

    Step 2. Take the midpoint O of PQ and draw a circle keeping O as the centre of the circle and radius 3cm.

    Step 3. Draw the perpendicular bisectors of PO and OQ which intersects at points R and S, i.e., R and S are the mid points of OP and OQ respectively.

    Step 4. Draw a circle with center R and radius RP.

    Step 5. Draw a circleWith center S and radius SQ.

    Step 6. Here the circle with centre O will be intersecting the other circles with centre R and S at the points A, B, C, and D.

    Step 7. Join PA, PB, QC, and QD.

    Class 10 maths chapter 11 constructions Ex 11.3-4

    Here, PA, PB, QC, and QD are the tangents required.

  3. Draw a line segment AB of length 8 cm. Taking A as the center, draw a circle of radius 4 cm and taking B as the center, draw another circle of radius 3 cm. Construct tangents to each circle from the center of the other circle.

    Solutions:

    Given:

    To draw a line segment AB of length 8 cm and then draw 2 circle of radius 4 cm and 3 cm, taking A and B as the centre of the circles respectively. And later construct tangents to each circle from the center of the other circle.

    Sample Figure:

    Class 10 maths chapter 11 constructions Ex 11.3-5

    Construction:

    Step 1.Draw a line segment AB of length 8 cm.

    Step 2. Now, draw the perpendicular bisector of AB which intersects it at C.

    Step 3. Draw a circle with the center, C and radius CA.

    Step 4. Draw two circles with centers A and B of radius 4 cm and 3 cm respectively, such that they intersect the circle with centre C at the points P, Q, R and S.

    Step 5. Join AR, AS, BP and BQ

    Class 10 maths chapter 11 constructions Ex 11.3-6

    Here, AR, AS, BP and BQ are the tangents required.

  4. Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its center.

    Solutions:

    Given:

    To draw a circle of radius 3.5 cm and two tangents to the circle from a point P at a distance of 6.2 cm from its center.

    Sample Figure:

    Class 10 maths chapter 11 constructions Ex 11.3-7

    Construction:

    Step 1. Draw a circle with center O and radius 3.5 cm.

    Step 2. Mark a point P outside the circle such that OP = 6.2 cm

    Step 3. Join OP. and draw the perpendicular bisector of OP say XY, cutting OP at Q.

    Step 4. Draw a circle with center Q and radius PQ or OQ, such that it intersects the given circle at the points T and T`.

    Step 5. Join PT and PT` to obtain the required tangents.

    Class 10 maths chapter 11 constructions Ex 11.3-8

    Here, PT and PT` are the tangents.

  5. Draw a pair of tangents to a circle of radius 4.5 cm, which are inclined to each other at an angle of 45o.

    Solutions:

    Given:

    To draw a circle or radius 4.5 cm and a pair of tangents to the circle at an inclination of 45o to each other.

    Sample figure:

    Class 10 maths chapter 11 constructions Ex 11.3-9

    Construction:

    Step 1. First, draw a circle with center O and radius 4.5 cm.

    Step 2. Draw a diameter of the circle, say AOB.

    Step 3. Construct an ∠BOC=45O such that, radius OC cuts the circle at C.

    Step 4. Draw AM⊥AB and CN⊥OC. Let AM and CN intersect each other at X.

    Class 10 maths chapter 11 constructions Ex 11.3-10

    Here, AX and CX are the pairs of tangents to the circle inclined to each other at an angle of 45o

  6. Draw a right triangle ABC in which AB = 6 cm, BC = 6 cm and ∠B=90O. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.

    Solutions:

    Given:

    To draw a right triangle ABC in which AB = 6 cm, BC = 6 cm and ∠B=90O. And then, draw: BD perpendicular from B on AC and a circle passing through the points B, C and D. Later construct tangents from A to this circle.

    Sample figure:

    Class 10 maths chapter 11 constructions Ex 11.3-11

    Construction:

    Step 1. Draw a line segment AB of length 6 cm

    Step 2. Draw ∠ABX=90O at B,.

    Step 3. Draw an arc cutting the ray BX at C, with center B and radius 8 cm,.

    Step 4. Join AC. Here, ΔABC is the required triangle.

    Step 5. Draw BD⊥AC from B,.

    Step 6. Draw the perpendicular bisector of BC such that it cuts BC at O.

    Step 7. Draw a circle with center O and radius OB or OC. Such that the circle passes through B, C and D. Here, we get the required circle.

    Step 9. Join OA. And draw the perpendicular bisector of OA such that it cuts OA at E.

    Step 11. Draw a circle intersecting the circle with center O at B and F with center E and radius AE or OE.

    Step 12. Now Join AF.

    Class 10 maths chapter 11 constructions Ex 11.3-12

    Here, AB and AF are the tangents.

1 Comment

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