if two equal chords AB and CD intersect within the circle. prove that AD=BC

Question

Answer

i think intersect nahi bisect hona chaahiye...

Answer

is there any fig .of question ?

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kya tmhare paas fig. hai ? question ka

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Let be intersect point is E and draw a perpendicular Ol and OM on Ab and cd then congruent ∆OlE=~∆OME So OL=OMThen AB=CD

Answer

Hints

Construction - 1. Draw perpendicular bisector of AB from center O

2. Draw for CD also.

3. Join the mid points of AB (say G) and CD (say F) .

PROVE - prove AG and CF equal so that AB will be equal to CD

then,

Arc AB = Arc CD. (1)

Arc AD + Arc BD = Arc AB

Arc CB + Arc BD = arc CD

So,

arc AD + arc BD = Arc CB + arc BD

Hence

arc AD = arc CB

Sending soon the image of complete solution.

Answer

PLZZZZZ DO THIS!!

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give me figure

Answer

Proof that AD = BC when two equal chords AB and CD intersect within the circle:

Given: Two equal chords AB and CD intersect within the circle.

To Prove: AD = BC

Proof:

Step 1: Let O be the center of the circle, and let the chords AB and CD intersect at point P.

Step 2: Draw the radii OA, OB, OC, and OD. Since OA and OB are radii of the same circle, they are equal in length. Similarly, OC and OD are also equal in length.

Step 3: Since AB and CD are equal chords, they are equidistant from the center of the circle. This implies that the distances from the center to points A and B are equal, as well as the distances from the center to points C and D.

Step 4: Consider triangles OPA and OPB. We know that OA = OB (radii of the same circle) and OP is common to both triangles.

Step 5: By the Side-Angle-Side (SAS) congruence criterion, triangles OPA and OPB are congruent.

Step 6: Therefore, angle OAP is equal to angle OBP.

Step 7: Similarly, considering triangles OPC and OPD, we can conclude that angle OCP is equal to angle ODP.

Step 8: Since angle OAP is equal to angle OBP and angle OCP is equal to angle ODP, the opposite angles of quadrilateral ABCD are equal.

Step 9: Quadrilateral ABCD is a cyclic quadrilateral since its vertices lie on a circle. In a cyclic quadrilateral, the opposite angles are supplementary.

Step 10: Therefore, angle DAP + angle BCP = 180 degrees.

Step 11: Since angle DAP and angle BCP are equal (opposite angles of the cyclic quadrilateral), we can write: 2 * angle DAP = 180 degrees.

Step 12: Solving for angle DAP, we get: angle DAP = 90 degrees.

Step 13: Since angle DAP is a right angle, triangle DAP is a right triangle.

Step 14: In a right triangle, the hypotenuse is the longest side.

Step 15: Therefore, AD is the longest side of triangle DAP.

Step 16: Similarly, we can prove that BC is the longest side of triangle BCP.

Step 17: Since AD is the longest side of triangle DAP and BC is the longest side of triangle BCP, we can conclude that AD = BC.

Conclusion: Therefore, it is proved that AD = BC when two equal chords AB and CD intersect within the circle.

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