if you want to remove an article from website contact us from top.

    2.construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6cm and measure its length.also verify the measurement by actual calculation.

    Mohammed

    Guys, does anyone know the answer?

    get 2.construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6cm and measure its length.also verify the measurement by actual calculation. from screen.

    Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

    Click here👆to get an answer to your question ✍️ Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

    Question

    Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of  radius 6 cm and measure its length. Also verify the measurement by actual calculation. 

    (1)Draw two concentric circle C

    Easy Open in App Solution Verified by Toppr 1 ​ and C 2 ​ with common center

    0 and radius 4cm and 6cm

    (2) Take a point P on the outer circle C

    2 ​ and join OP.

    (3) Draw the bisector of OP which bisect OP at M'.

    (4) Taking M' as center and OM' as radius draw a dotted circle which

    cut the inner circle C

    1 ​

    at two point M and P.

    (5) Join PM and PP'.  Thus, PM and PP' are required tangent.

    On measuring PM and PP'.

    PM=PP ′ =4.4cm Bycalculation: InΔOMP,∠PMO=90 0 PM 2 =OP 2 −OM 2

    (bypythagorastheorem)

    PM 2 =(6) 2 −(4) 2 =36−16=20 PM 2 =20cm PM= 20 ​ =4.4cm Hence,

    thelengthofthetangentis4.4cm

    Was this answer helpful?

    365 38

    स्रोत : www.toppr.com

    Construct a Tangent to a Circle of Radius 4 Cm Form a Point on the Concentric Circle of Radius 6 Cm and Measure Its Length. Also, Verify the Measurement by Actual Calculation.

    Construct a Tangent to a Circle of Radius 4 Cm Form a Point on the Concentric Circle of Radius 6 Cm and Measure Its Length. Also, Verify the Measurement by Actual Calculation.

    Advertisement Remove all ads

    Construct a tangent to a circle of radius 4 cm form a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.

    Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm ?

    Advertisement Remove all ads

    SOLUTION 1

    Steps of Construction

    Step 1: Mark a point O on the paper

    Step 2: With O as center and radii 4cm and 6cm, draw two concentric circles.

    Step 3: Mark a point P on the outer circle.

    Step 4: Join OP.

    Step 5: Draw the perpendicular bisector XY of OP, cutting OP at Q.

    Step 6: Draw a circle with Q as center and radius OQ (or PQ), to intersect the inner circle in points T and T’.

    Step 7: Join PT and PT’.

    Here, PT and PT’ are the required tangents.

    PT = PT’ 4.5 cm (Approx)

    Verification by actual calculation

    Join OT to form a right ΔOTP (Radius is perpendicular to the tangent at the point of contact)

    In right ΔOTP, OP2=OT2+PT2

    (Pythagoras Theorem)

    ⇒PT=OP2-OT2

    ⇒PT=62-42=36-16=20 ≈ 4.5cm

    (OP = 6 cm and OT = 4cm)

    SOLUTION 2

    Steps of construction:

    1. Draw two concentric circles with centre O and radii 4 cm and 6 cm. Take a point P on the outer circle and then join OP.

    2. Draw the perpendicular bisector of OP. Let the bisector intersects OP at M.

    3. With M as the centre and OM as the radius, draw a circle. Let it intersect the inner circle at A and B.

    4. Join PA and PB. Therefore,

    PA¯ and PB¯

    are the required tangents.

    Concept: Construction of Tangents to a Circle

    Is there an error in this question or solution?

    Chapter 13: Constructions

    Q 10 Q 9

    APPEARS IN

    RS Aggarwal Secondary School Class 10 Maths

    Chapter 13 Constructions

    Q 10

    2012-2013 (March) Delhi set 3 (with solutions)

    VIDEO TUTORIALS

    VIEW ALL [6] view

    Video Tutorials For All Subjects

    Construction of Tangents to a Circle

    video tutorial 00:02:42

    Construction of Tangents to a Circle

    video tutorial 00:04:46

    Construction of Tangents to a Circle

    video tutorial 00:09:39

    Construction of Tangents to a Circle

    video tutorial 00:05:39

    Construction of Tangents to a Circle

    video tutorial 00:02:06

    Construction of Tangents to a Circle

    video tutorial 00:09:40 Advertisement Remove all ads

    स्रोत : www.shaalaa.com

    Ex 11.2, 2

    Ex 11.2, 2 Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation. Steps of construction Draw a circle of radius 4 cm with center O Draw concentric circle of radius 6 cm,

    Check sibling questions

    Ex 11.2, 2 - Chapter 11 Class 10 Constructions (Term 2)

    Last updated at July 14, 2020 by Teachoo

    Next: Ex 11.2, 3 →

    Facebook Whatsapp

    Transcript

    Ex 11.2, 2 Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation. Steps of construction Draw a circle of radius 4 cm with center O Draw concentric circle of radius 6 cm, with center O Mark point P on the larger circle 3. Join PO. Make perpendicular bisector of PO Let M be the midpoint of PO. 4. Taking M as centre and MO as radius, draw a circle. 5. Let it intersect the given circle at points Q and R. 6. Join PQ and PR. ∴ PQ and PR are the required two tangents. After measuring, lengths of tangents PQ and PR are 4.47 cm each Finding lengths of PQ and PR Join OQ and OR Since tangent is perpendicular to radius ∠PQO = 90° & ∠PRO = 90° Thus, Δ PQO is a right angled triangle, And, PO = radius of bigger circle = 6 cm and OQ = radius of smaller circle = 4 cm By Pythagoras theorem PO2 = PQ2 + OQ2 62 = PQ2 + 42 36 = PQ2 + 16 PQ2 = 36 – 16 PQ2 = 20 PQ = √20 PQ = 2 × 2.236 PQ = 4.47 cm Similarly, PR = 4.47 cm Justification We need to prove that PQ and PR are the tangents to the circle. Join OQ and OR. Now, ∠PQO is an angle in the semi-circle of the blue circle And we know that, Angle in a semi-circle is a right angle. ∴ ∠PQO = 90° ⇒ OQ ⊥ PQ Since OQ is the radius of the circle, PQ has to be a tangent of the circle. Similarly, PR is a tangent of the circle.

    Article by

    Davneet Singh

    Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.

    स्रोत : www.teachoo.com

    Do you want to see answer or more ?
    Mohammed 5 month ago
    4

    Guys, does anyone know the answer?

    Click For Answer