Circle

@rishab1988: because angle ADC got bisected in two equal angles by 'bisector' DE, making equal angles of ADE and EDC.

Hi there...unfortunately, I still don't understand how ADE = DCE...can you please explain?

Thank you.

@martie_11: For this you may like to visit the 'youtube' link provided in the first few messages, detailing the theorem.

That theorem was what I was looking for!.Thanks everyone.Any more questions like this will be really appreciated.

goyalsau wrote:angle ADE = Angle DCE

Because of Alternate Segment Theorem , - if you have any doubts look at the link https://www.youtube.com/watch?v=nwOSsjLDACQ

Lets Assume Angle AED = e

and angle ADE = x,
which means ADE = DCE = EDC = x

in Triangle DEC

x + x + 180 - e = 180

e = 2x


in Triangle AED

24 + e + x = 180

24 + 3x = 180

x = 52

Angle ACB is equal to 90

90 = 52 + theta

theta = 38

man!

Rahul@gurome wrote:
BC is neither a tangent to the large circle nor to the smaller.
BC would've been the tangent at point C only if joining the radius of the circle and C resulted in a 90° the line and BC. But as AC is perpendicular BC at point C and AC is not a part of radius of any of the circles, BC is not tangent to any of them.

I just Want to rephrase what you said, to clear my understanding of Tangent,

line passing through the circumference of the circle will be a tangent to the circle if the angle formed by joining the radius of the circle and the line is 90 Degree at that particular point.

IF The line if passing through the circumference but is not making a 90 degree angle with line that will be made by joining that particular point and the center of the circle then , WE can not call that line a tangent.

Guys please Correct me if am wrong ... And if am right then also please do let me know..........

goyalsau wrote:

Rahul@gurome wrote:
BC is neither a tangent to the large circle nor to the smaller.
BC would've been the tangent at point C only if joining the radius of the circle and C resulted in a 90° the line and BC. But as AC is perpendicular BC at point C and AC is not a part of radius of any of the circles, BC is not tangent to any of them.

I just Want to rephrase what you said, to clear my understanding of Tangent,

line passing through the circumference of the circle will be a tangent to the circle if the angle formed by joining the radius of the circle and the line is 90 Degree at that particular point.

IF The line if passing through the circumference but is not making a 90 degree angle with line that will be made by joining that particular point and the center of the circle then , WE can not call that line a tangent.

Guys please Correct me if am wrong ... And if am right then also please do let me know..........

Absolutely correct.