Question

let A be the point of intersection of two intersecting circles with Centre O and q tangents at a to the two circles meet the circle again at B and C respectively let point P be located show that AO PQ is a parallelogram prove that P is the circumcenter of triangle ABC

Answer 1

Given two circles with centre’s O and Q Let the circles intersect at point A Given that the tangents at A to the two circles meet them at B and C such that AOQP forms a parallelogram. AQ⊥AB {Radius perpendicular to tangent} AQ||OP (Given) Hence OP⊥AB We know that the line drawn from the centre to the chord bisects the chord. Hence OP bisects AB That is OP is perpendicular bisector of AB Similarly PQ is perpendicular bisector of AC Since the perpendicular bisectors intersect at P. Thus P is the circumcentre of ΔABC.

Answer 2

Answer:

Step-by-step explanation: