AB is a chord of the circle x2 + y2 = 9 The tangents at A and B - Maths - Conic Sections

Question

AB is a chord of the circle x2 + y2 = 9 The
tangents at A and B intersect at C If M (1,2) is the mid-point of
AB than the area of triangle ABC is = ?

Rahul Raj · Accepted Answer

dear student

the diagram will be

circle centre is (0,0) and radius =3OM=(1-0)2+(2-0)2=5OA=radius=3AM=OA2-OM2=9-5=2length of chord AB=2*2=4tanθ=AMOM=25further angle CAB=angle BAO (angles in alternate segment)tanθ=CMAM=25CM2=25CM=45area of triangle ABC=12×AB×CM=12×4×45=85

regards

AB is a chord of the circle x2 + y2 = 9 . The tangents at A and B intersect at C . If M (1,2) is the mid-point of AB than the area of triangle ABC is = ?

AB is a chord of the circle x² + y² = 9 . The tangents at A and B intersect at C . If M (1,2) is the mid-point of AB than the area of triangle ABC is = ?