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help please (1 Viewer)

Thread starter mathsbrain
Start date Apr 5, 2014

M

mathsbrain

Member

#1

Please help

PHP:

Axio

=o

#2

$a)\: \angle BPA=\angle PCA\: (angles\: in\: alternate\: segments)\\ \therefore \Delta BPA|||\Delta PCA\: (AAA)\\ \frac{PA}{AC}=\frac{AB}{PA}\\ PA^{2}=AC\cdot AB\\ \angle BQA =\angle QCA\: (angles\: in\: alternate\: segments)\\ \therefore \Delta BQA|||\Delta QCA\: (AAA)\\ \frac{AQ}{AC}=\frac{AB}{AQ}\\ AQ^{2}=AC\cdot AB\\ \therefore PA^{2}=AQ^{2}\\ PA=AQ\\ \\ b)\: Using\: part\: a):\: 12^{2}=6AC\\ AC=24$

Last edited: Apr 5, 2014

Sy123

This too shall pass

#3

mathsbrain said:
Please help

PHP:

By tangent-secant theorem

$AP^2 = AB \cdot AC$

$AQ^2 = AB \cdot AC$

$\therefore \ AP = AQ$

$\\ $Then using the first equation$ \ 12^2 = 6 \cdot AC$

Axio

=o

#4

Sy123 said:
By tangent-secant theorem

$AP^2 = AB \cdot AC$

$AQ^2 = AB \cdot AC$

$\therefore \ AP = AQ$

$\\ $Then using the first equation$ \ 12^2 = 6 \cdot AC$

That's a much better method ^...

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