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Kishore answered 5 year(s) , 7 month(s) ago

The height of a cone is 30 cm. A small cone is cut off


Given height of the cone = 30 cm
Let the small cone is cut off at a height ‘h’ from the top
Let the radius of big cone be r 1 and small cone be r 2.
Volume...

Asked by Keisam

Oct 30

  • 1 Answer
  • 4 Likes
  • 68626 Views
Raghunath answered 4 year(s) , 3 month(s) ago

In a circle of radius 5 cm , AB and AC are two chords such that AB = BC = 6 cm. Find the length of chord BC.


Given
 AB and AC are two equal words of a circle, therefore the centre of the circle lies on the bisector of ∠BAC.

⇒ OA is the bisector of ∠BAC.

Again, the internal bi

...

Asked by Abhijeet

Mar 3

  • 2 Answers
  • 3 Likes
  • 37862 Views
Syeda answered 1 year(s) ago

Prove that the quadrilateral formed by the internal angle bisectors of any quadrilateral is cyclic?

Answer.


Given a quadrilateral ABCD with internal angle bisectors AF, BH, CH
and DF of angles A, B, C and D respectively and the points E, F, G
and H form a quadrilateral EFGH.

...

Asked by Rushil

Jan 4

  • 2 Answers
  • 3 Likes
  • 36603 Views
Agam answered 1 year(s) , 1 month(s) ago

AB and CD are two chords of a circle, such that AB=6 cm, CD =12 cm


Given chords AB=6 cm, CD =12 cm and AB||CD
Draw OP⊥ AB. Let it intersect CD at Q and AB at P
∴ AP = PB = 3 cm and CQ = DQ = 6 cm [Since perpendicular draw from the centre of the chord bis...

Asked by Keisam

Oct 24

  • 2 Answers
  • 4 Likes
  • 33307 Views
Syeda answered 1 year(s) ago

prove that if non parallel sides of a trapezium are equal than prove that it is cyclic


In ΔAED and ΔBFC,
AD = BC     (Given)
DE = CF    (Distance between parallel sides is same)
∠AED = ∠BFC = 90°
ΔAED ≅ ΔBFC  (RHS Congruence criterion)
Hence ∠DAE = ∠...

Asked by Ravinder

Mar 8

  • 2 Answers
  • 2 Likes
  • 33098 Views
Kishore answered 5 year(s) , 3 month(s) ago

A chord of a circle is equal to the radius of the circle


In ΔOAB,
AB = OA = OB (radii)
Hence ΔOAB is an equilateral triangle
That is each angle of ΔOAB is 60°
∴ ∠AOB = 60°
∠AOB = 2 ∠ACB [Angle subtended by an arc of a ci...

Asked by Regi

Mar 5

  • 2 Answers
  • 3 Likes
  • 25358 Views
Raghunath answered 4 year(s) , 3 month(s) ago

ABC is a right angled triangle, right angled at A. a circle is inscribed in it. the length of two sodes containing angle A is 12 cm and 5 cm. find the radius.

Consider ABC be the right angled triangle such that ∠A = 90° and AB = 5cm, AC = 12 cm. 

And O be the centre and r be the radius of the incircle.

AB, BC and CA are tangents to the cir

...

Asked by Anoop

Feb 18

  • 2 Answers
  • 0 Like
  • 25126 Views
Raghunath answered 4 year(s) , 3 month(s) ago

Prove that there is one and only one circle passing trough three given non-collinear points.

Theorem: There is one and only one circle passing through three given non-collinear points.

Given: Three non collinear points P, Q and R

To

...

Asked by Ritik

Mar 2

  • 1 Answer
  • 2 Likes
  • 22865 Views
Syeda answered 1 year(s) ago

circle drawn on any one of the equal sides of an isosceles triangle

Given: ΔABC is an isosceles triangle with AB = AC. A circle is drawn taking AB as the diameter which intersects the side BC at D.

To prove: BD = DC

Construction: Join AD<

...

  • 4 Answers
  • 2 Likes
  • 21591 Views
Raghunath answered 4 year(s) , 2 month(s) ago

If two circles intersect at two points, then prove that their centres lie on the perpendicular bisector of the common chord.


Let two circles O and O' intersect at two points A and B so that AB is the common chord of two circles and OO' is the line segment joining the centres
Let OO' intersect AB at M
Now Draw l...

Asked by Adithyan

Mar 21

  • 1 Answer
  • 0 Like
  • 21042 Views
Ramesh answered 5 year(s) , 1 month(s) ago

if a pair of opposite sides of a cyclic quadrilateral are equal, then prove that the other two sides are parallel

Sol:

Given: Cyclic quadrilateral ABCD such that AD = BC
To Prove: AB parallel to CD
Construction: Join BD
...

Asked by Himalaya

Feb 22

  • 1 Answer
  • 2 Likes
  • 19162 Views
Ramesh answered 5 year(s) , 2 month(s) ago

PROVE THAT THE SUM OF THE OPPOSITE ANGLES OF A CYCLIC QUADRILATERAL ARE SUPPLEMENTARY??????

Sol :
Given : Let ABCD is cyclic quadrilateral.
To prove : ∠A + ∠C = 180°  and ∠B + ∠D = 180°.
Construction : join OB and OD.

Proof : ∠BOD = 2 ∠BAD
     ∠BAD = 1...

Asked by Khushboo

Dec 17

  • 1 Answer
  • 6 Likes
  • 19092 Views
Bhawna answered 4 year(s) , 2 month(s) ago

ABC is an isosceles triangle inscribed in a circle


Draw AD⊥BC
Hence D is the midpoint of BC
That is BD = DC = (1/2) BC
Therefore, BD = DC = 7 cm
In right triangle ADB, by Pythagoras theorem we have
AB 2...

Asked by Rohit

Mar 9

  • 2 Answers
  • 0 Like
  • 15706 Views
Agam answered 1 year(s) , 10 month(s) ago

Prove that ,in a cyclic trapezium,the non-parallel sides are equal

We know that the angle at the circumference is 1/2 of the centre angle .similarly ab is parallel to dc

Asked by Ritika

Mar 5

  • 5 Answers
  • 0 Like
  • 15388 Views
Raghunath answered 4 year(s) , 3 month(s) ago

Prove that the bisectors of angles formed by the producing opposite sides of a cyclic quadrilateral (provided that they are not ll) intersect arch other at right angle.


A cyclic quadrilateral ABCD whose opposite sides when produced intersect at the [points P and Q]. The bisectors PF and QF of ∠P and ∠Q respectively at F
produce QF to meet AB at E
In ΔQDG...

Asked by Abhijeet

Mar 3

  • 2 Answers
  • 3 Likes
  • 13457 Views
Kishore answered 5 year(s) , 7 month(s) ago

Equal chords of a circle are equidistant from the centre or centres


Given a circle with centre O and chords AB = CD
Draw OP⊥ AB and OQ ⊥ CD
Hence AP = BP = (1/2)AB and CQ = QD = (1/2)CD
Also ∠OPA = 90° and ∠OQC = 90°
Since AB = CD
...

Asked by Kanishka

Nov 10

  • 1 Answer
  • 0 Like
  • 12212 Views
Ramesh answered 4 year(s) , 4 month(s) ago

Find angle BOC and BDC.

Sol:
∠ABC = 50° ⇒ ∠ACB = 50° [Isosceles triangle property]

∠BAC = 180° - (50° + 50°) = 80°

∠BOC = 2 x 80° = 160° [Angle made by an arc at the centre of a circle is twice...

Asked by Priya

Jan 13

  • 1 Answer
  • 4 Likes
  • 9795 Views
Shivam answered 4 year(s) , 2 month(s) ago

O is the centre of circle, angle bco=30º

We know that angle subtended by an arc of a circle at the centre is double the angle subtended by it on remaining part of the circle.
Arc CD subtends ∠COD at centre and subtends ∠BCD at B on the circle...

Asked by Vivek

Mar 12

  • 3 Answers
  • 1 Like
  • 9590 Views
G commented 5 year(s) , 5 month(s) ago

Prove that the circle drawn with any side of a rhombus as diameter


Let ABCD be the rhombus with AC and BD as diagonals intersecting at point O.
Recall that, diagonals of a rhombus bisect each other at right angles.
∴ ∠AOB = ∠BOC = ∠COD = ∠AOD = 90°...

Asked by G

Dec 25

  • 1 Answer
  • 1 Like
  • 9388 Views
Jay commented 5 year(s) , 5 month(s) ago

Two tangents segment PA and pB are drawn to a circle

here, in figure,
      angle APB= 120°
so,angle APO= 60 °
Here, triangle APO is right angle triangle.
By the formulas of trigonometric ratios:-
   AP/ OP = cos 60 °=1/2...

Asked by Tanisha

Jan 5

  • 3 Answers
  • 0 Like
  • 9184 Views
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