# Thread: help needed for question on circles

1. ## help needed for question on circles

hi all, here goes the question. A,b,c,d are four points on the circumference of the circle. P is the point of intersection of lines ac and bd. St is the tangent of the circle at point d. Given that angle adt=60 degrees and angle cdb=40 degrees, find angle apd. The centre of circle is not given.

2. Hm... Scizor... you had a metal coat?

Okay, serious things now.

Make a sketch.

You'll see from your sketch that angle ADB is equal to (90 - 60). 90 because ST is a tangent and this is divided into two angles, one being 60 degrees.

Then, using the properties of angles in a circle, we know that angle CBD and angle CAD are equal, hence, angle CAD = 40 degrees (Which is also angle PAD)

Now, you'll also see that PAD forms a triangle. You have angle PAD, angle PDA and you need to find angle APD. Can you find it?

Spoiler:
Angle APD = 180 - (40+60) = 80 degrees

3. just a question, why are you so sure that p is indeed the centre of the circle? Otherwise all the properties of circle cannot be applied then.

4. I'm not assuming that P is the centre of the circle. I'm considering P as a vertex in a triangle.

5. Originally Posted by Unknown008
I'm not assuming that P is the centre of the circle. I'm considering P as a vertex in a triangle.
oic cheers for your reply. Much appreciated.

6. You're welcome