Need help with Plane Geometry (1 Viewer)

[lilkiwifruit]

Hey I'm really really stuck on two questions, I would really appreciate your help

1. PA and PB are two tangents to a circle and X is the midpoint of the minor arc AB. Prove that XA bisects angle PAB.

2. AB and CD are parallel chords of a circle. The tangent at B meets CD produced at E. Prove that triangle ABC and triangle DBE are similar.

** If you have the new senior mathematics textbook, its exercise 20 c) question 33 and 34.

 

[shafqat]

Hey I'm really really stuck on two questions, I would really appreciate your help

1. PA and PB are two tangents to a circle and X is the midpoint of the minor arc AB. Prove that XA bisects angle PAB.

2. AB and CD are parallel chords of a circle. The tangent at B meets CD produced at E. Prove that triangle ABC and triangle DBE are similar.

** If you have the new senior mathematics textbook, its exercise 20 c) question 33 and 34.

1. Angle PAX = angle XBA (alt segment)
Also XAB is isos (equal chords on equal arcs)
So angle xab = angle xba = angle pax

2. angle dbe = angle bcd (alt segment) = angle abc (|| lines)
angle bde = angle bac (ext angle cycl quad)
AA
//

 

[lilkiwifruit]

1. Angle PAX = angle XBA (alt segment)
Also XAB is isos (equal chords on equal arcs)
So angle xab = angle xba = angle pax

2. angle dbe = angle bcd (alt segment) = angle abc (|| lines)
angle bde = angle bac (ext angle cycl quad)
AA
//

thank you soo much!

 

[velox]

hah more st ives ppl.

Ex st ives person right here.

 

[lilkiwifruit]

Another question has just popped up...I would really hope someone could help me with this..

this is exercise 20c) Question 36 in the textbook:

10 equal circular discs can just bbe placed tightly within a frame in the form of an equilateral triangle. None of them touch the frame; the tenth, in the centre, touches 6 of the other discs. If the internal sides of the frame are each of length measure R, express the radius of each circular disc in terms of R, and show that the outside perimeter of the figure which remains when the frame is removed is
11/12 (3- √3)╥R