ON 4 gram, PKT is a common tangent to both circles at K(a; b). The centres of bot on the line y = x. The equation of the circle centred at O is x² + y² =180- 2 1 s of the circle is three times that of the circle centred at M. Determine:
4.3.1 Write down the length of OK in surd form.
Show that K is the point (-12;-6).
4.3.2 P. M
4.3.3 K(a; b) O y= 1 The equation of the common tangent, PKT, in the form y=mx+c The coordinates of M The equation of the smaller circle in the form (x-a)²+(y-b)² = r²
For which value(s) of r will another circle, with equation x² + y² = r², intersect the circle centred at M at two distinct points? Another circle, x² + y² +32x+16y+240=0, is drawn.
Prove by calculation tha this circle does NOT cut the circle with centre M(-16; -8).​