Question

In the given figure AD is diameter of the circle whose centre is O and AB ||CD prove that AB=CD

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Any straight line segment that travels through the centre of a circle and has endpoints that are on the circle is said to have a diameter.

AB = AC + CD = 2AC = BD = CD. Hence, we have proved that AB = CD.

Since AD is the diameter of the circle with center O, then by definition, angle AOD is a right angle.

Since AB is parallel to CD, then angle ABD and angle ACD are alternate interior angles and are therefore congruent. Similarly, angle CBD and angle CDA are alternate interior angles and are congruent.

Since the angles ACD and CDA are congruent, then the triangles ACD and CBD are similar (by the angle-angle-angle similarity criterion).

By similarity, we have:

AC/BC = CD/BD

But, since AD is a diameter, we have AC + CD = AD and BC + CD = BD.

Adding these two equations together, we get:

AC + BC + 2CD = AD + BD

But, since AC = BC (as AB is parallel to CD), we have:

2AC + 2CD = AD + BD

Substituting AC/BC = CD/BD, we get:

2AC + 2(AC/CD)CD = AD + BD

Simplifying, we get:

2AC + 2AC = AD + BD

4AC = AD + BD

But, since AD is the diameter, we have AD = 2AC.

Substituting, we get:

4AC = 2AC + BD

2AC = BD

Therefore, AB = AC + CD = 2AC = BD = CD. Hence, we have proved that AB = CD.

for such more question on diameter

https://brainly.in/question/2974270

#SPJ2