Heya! In the given figure , ABC is a triangle in which AB = AC. Also a circle passing through B and C intersects the sides AB and AC at the points D and E respectively. Prove that AD = AE.
~Thanks in advance! :)

See Below.

Step-by-step explanation:

We are given that ABC is a triangle in which AB = AC.

A circle passing through B and C also intersects the sides AB and AC at points D and E respectively.

And we want to prove that AD = AE.

By the secant-secant theorem (shown below), we know that:

We are given that AB = AC. So, by substitution:

And by dividing both sides by AB (AB ≠ 0), we acquire:

Q.E.D.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

35-60 students are taking math.