Question

if two cirlcle intersect each other at a point p and q respectively secants drawn through P Q and imtersect circle at point A B and D C.prove that angleADC+angleBCD=180

Answer 1

Step-by-step explanation:

LET Angle TPQ =@(using this sign instead of theta) Therefore angle TQP also = @

Also PT is tangent to the circle therefore, the angle between the the tangent PT and chord PA is equal to the the angle made by the chord on the opposite segment (angle PBA=@) similarly angle QBA =angle TQP=@

Also angle PTQ=180–(2×@) by angle sum property of triangle.

In quadrilateral TQBP, angle T and B add upto 180 therefore TQBP is a cyclic quadrilateral.