हिंदी

In the Given Figure, Chord Ef || Chord Gh. Prove That, Chord Eg ≅ Chord Fh. Fill in the Blanks and Write the Proof. - Geometry Mathematics 2

Advertisements
Advertisements

प्रश्न

In the given figure, chord EF || chord GH. Prove that, chord EG ≅ chord FH. Fill in the blanks and write the proof. 

योग

उत्तर

Proof: Draw seg GF.

∠EFG = ​∠FGH .....property of alternate angles of parallel lines      (I)

∠EFG = ​ \[\frac{1}{2}m\left( arc EG \right)\]         .....inscribed angle theorem (II)
∠FGH = ​ \[\frac{1}{2}m\left( arc FH \right)\]       .....inscribed angle theorem (III)
∴ m(arc EG) = \[m\left( arc FH \right)\]        from (I), (II), (III)
chord EG ≅ chord FH        ....  Chords corresponding to congruent arcs of a circle are congruent.
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Circle - Problem Set 3 [पृष्ठ ८८]

APPEARS IN

बालभारती Geometry (Mathematics 2) [English] 10 Standard SSC Maharashtra State Board
अध्याय 3 Circle
Problem Set 3 | Q 17 | पृष्ठ ८८

संबंधित प्रश्न

A circle touches the side BC of a ΔABC at a point P and touches AB and AC when produced at Q and R respectively. As shown in the figure that AQ = `1/2` (Perimeter of ΔABC).


In the given figure, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects PQ at A and RS at B. Prove that ∠AOB = 90º


Write True or False. Give reasons for your answers.

A chord of a circle, which is twice as long as its radius, is a diameter of the circle.


Write True or False. Give reason for your answer.
A circle is a plane figure.


If AB, AC, PQ are tangents in Fig. and AB = 5cm find the perimeter of ΔAPQ.


From an external point P, tangents PA and PB are drawn to the circle with centre O. If CD is the tangent to the circle at point E and PA = 14 cm. Find the perimeter of ABCD.


The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4cm,5cm and 7cm respectively. Determine the length of fourth side.


In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. Calculate the sizes of:

  1. ∠AOB, 
  2. ∠ACB,
  3. ∠ABC.


In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6cm, BC=7cm and CD=4 cm. Find AD.


In the given figure, PA and PB are the tangent segemtns to a circle with centre O. Show that he points A, O, B and P are concyclic.


In the given figure, a triangle ABC is drawn to circumscribe a circle of radius 3 cm such that the segments BC and DC into which BC is divided by the point of contact D, are of
lengths 6cm and 9cm respectively. If the area of 2 ΔABC = 54cm2 then find the lengths of sides AB and AC.


In the given figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50°, find ∠AOC.


AB is a chord of a circle with centre O , AOC  is a diameter and AT is the tangent at A as shown in Fig . 10.70. Prove that \[\angle\]BAT = \[\angle\] ACB


Find the length of the chord of a circle in the following when: 

Radius is 1. 7cm and the distance from the centre is 1.5 cm 


Construct a triangle XYZ in which XY = YZ= 4.5 cm and ZX = 5.4 cm. Draw the circumcircle of the triangle and measure its circumradius.


Draw a circle of diameter 7 cm. Draw two radii of this circle such that the angle between these radii is 90°. Shade the minor sector obtained. Write a special name for this sector.


Find the missing values in the following table for the circles with radius (r), diameter (d) and Circumference (C).

radius (r) diameter (d) Circumference (C)
  24 m  

A line segment joining any point on the circle to its center is called the _____________ of the circle


Find the radius of the circle

Diameter = 24 cm


From the figure, identify two points in the interior.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×