CAIE A-Level Mathematics AS 1.3.2 Line Equation Forms Questions

Practise equations, properties and intersections of circles in the AS mathematics syllabus.

Exam points

use the equation of a circle
determine geometric properties of circles
solve intersections involving circles

[Maximum number: 2]

Points A(-2,3), B(3,0) and C(6,5) lie on the circumference of a circle with centre D.

Show that angle $A B C=90^{\circ}$ .

Gradient of $A B=-\frac{3}{5}$ , gradient of $B C=\frac{5}{3}$ or lengths of all 3 sides or vectors
Attempting to find required gradients, sides or
vectors
$m_{a b} m_{b c}=-1$ or Pythagoras or $\overrightarrow{A B} \cdot \overrightarrow{B C}=0$ or $\cos A B C=0$ from cosine rule
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CAIE A-Level Mathematics AS 1.3.2 Line Equation Forms Questions question 1