Question

Two circles with centres H and K are 12 cm apart, the radii are 4cm and 8 cm respectively, touching externally. PQT is a tangent to both circles. If angle HTP is A, then what are sin A, cos A and tanA

Answer 1

@jim_thompson5910 @ganeshie8

Answer 2

they have a common angle so you know the triangles are similar

Answer 3

so you'll want to set up a ratio and from that you can create an equation to find x

Answer 4

yes but that doesn't exactly help @mathmath333

Answer 5

Oh it helps plenty, actually. You have two similar triangles now. \(\triangle TPK\) and \(\triangle TQH\)

Answer 6

I know and I tried that, does it actually work?

Answer 7

The radius is the perpendicular bisector of the line TP

Answer 8

\[\triangle THQ \sim \triangle TKP\\So\\ \frac{ TH }{ HQ }=\frac{ TK }{ KP }\\\frac{ TH }{ 4 }=\frac{ TH+HK }{ 8 }\\\frac{ TH }{ 4 }=\frac{ TH+12 }{ 8 }\\\]

Answer 9

\[\frac{x+12}{8}=\frac{x}{4}\]