# Thread: circle geometry help

1. ## circle geometry help

http://www.boardofstudies.nsw.edu.au...extension1.pdf

can someone help me with question 5c with explanations such as reasons

2. Hello andy69 [IMG]file:///C:/Users/janet/AppData/Local/Temp/moz-screenshot-8.png[/IMG]
Originally Posted by andy69
http://www.boardofstudies.nsw.edu.au...extension1.pdf

can someone help me with question 5c with explanations such as reasons
In the attached diagram, $TK$ is a tangent at $P$ to the circle $C_1$. We have to prove that $\triangle PKL$ is isosceles.

Proof

$\angle LPK = \angle TPM$ (vertically opposite)
$=\angle PQM$ (alternate segment)

$=\angle KLP$ (exterior angle of a cyclic quadrilateral)

$\therefore \triangle PKL$ is isosceles.