circle geometry help 2

**andy69** · May 20th 2010, 10:48 PM

http://www.boardofstudies.nsw.edu.au...ths-ex1-07.pdf

question 4c with explanations

**Grandad** · May 21st 2010, 05:47 AM

Hello andy69

The question is shown in the diagram I have attached.

Proof

(i) $\angle QXB + \angle BXA + \angle AXP = 180^o$ (angles on a straight line)

$\angle BXA = 90^o$ (given)

$\therefore \angle QXB + \angle AXP = 90^o$

But $\angle PAX + \angle AXP = 90^o$ (angle sum of $\triangle APX$ )

$\therefore \angle QXB = \angle PAX$

$=\angle QBX$ (angles in same segment)

(ii) $BQ = XQ$ (isosceles $\triangle BQX$ , from part (i))

$\angle BXC = 90^o$ (given)

$\therefore X$ lies on a circle with diameter BC (angle in semicircle)

But $BQ = XQ$ (proven)

$\therefore Q$ is the centre of the circle through $B, \;X$ and $C$

$\therefore BQ = QC$

Grandad

**andy69** · May 21st 2010, 07:15 AM

Originally Posted by Grandad

Hello andy69

The question is shown in the diagram I have attached.

Proof

(i) $\angle QXB + \angle BXA + \angle AXP = 180^o$ (angles on a straight line)

$\angle BXA = 90^o$ (given)

$\therefore \angle QXB + \angle AXP = 90^o$

But $\angle PAX + \angle AXP = 90^o$ (angle sum of $\triangle APX$ )

$\therefore \angle QXB = \angle PAX$

$=\angle QBX$ (angles in same segment)

(ii) $BQ = XQ$ (isosceles $\triangle BQX$ , from part (i))

$\angle BXC = 90^o$ (given)

$\therefore X$ lies on a circle with diameter BC (angle in semicircle)

But $BQ = XQ$ (proven)

$\therefore Q$ is the centre of the circle through $B, \;X$ and $C$

$\therefore BQ = QC$

Grandad

hey thanks for the help you mind me asking how do you attach the pictures?

**Grandad** · May 21st 2010, 12:27 PM

Hello andy69

Originally Posted by andy69

hey thanks for the help you mind me asking how do you attach the pictures?

I have a program called MWSnap that enables me to capture any part of the screen, to clipboard. Paste it into Paint; crop as necessary; save as .jpg. Quick and simple. Another example attached!

Grandad

Thread: circle geometry help 2

LinkBack

Thread Tools

Display

circle geometry help 2

Similar Math Help Forum Discussions

[SOLVED] Circle Geometry II

Circle Geometry: Proving a line passes through centre of circle

Circle Geometry: Centre of Circle

Circle Geometry

Circle Geometry

Search Tags