Question

two circles intersect at two points A and B .xy is tangent at point P prove that CD is parallel to tangent xy ​

Answer 1

Step-by-step explanation:

Pzz send the proper pic....

I am not understanding....

Answer 2

Answer:

It is given that,

Two circle intersect at points A and B.

XY is a tangent at point P

From the figure attached below, we can

see that from point P of one of the two

circles, two segments PAC and PBD are

drawn which intersect another circle at

point C and D.

Also, join point A and B.

We know that according to the

alternate segment theorem the angle

between a chord and a tangent through one of the endpoints of the

chord is equal to the angle in the

alternate segment.

Here XY is a tangent

: angleAPX = angleABP (i)

Now, from the figure again we can see

that all the vertices of ABCD lie inside

the circle so it is a cyclic quadrilateral.

So, by the theorem that the sum of the

opposite angles of a cyclic

quadrilateral is 180°, we get

angle ABD + angleACD = 180° .. (ii)

Also, angleABD + angleABP = 180° [Linear

Pair] . (i)

Therefore, from (ii) & (iii), we get

angt ACD = angle ABP . (iv)

From (i) and (iv), we get,

angle ACD = angle APX

Since we know that when two lines are

parallel to each other and the angles

lying on the opposite sides of the

transverse line i.e., the alternate angles

are equal to each other, so we can

conclude that

XY // CD

Hence Proved.