Question

two tangents PQ and PR are drawn from an external point to circle with center O. balu said the quadrilateral QORP is a cycle. do you agree?​

Answer 1

Answer:

Step-by-step explanation:

yes this is because the sum of the opposite angles in quadrilateral QORP is 180.

Answer 2

Quadrilateral QORP is a cyclic quadrilateral.

Tangents = 2 = PR and PQ  ( Given)

Therefore, OR ⊥ PR and OQ ⊥ PQ

If we draw a line from the center of a circle to its a tangent line. Therefore, then the line always perpendicular to the tangent line

Hence,

∠ORP=∠OQP =90°

∠ORP+∠OQP =180°

So, QOPR is cyclic quadrilateral.

If the sum of opposite angles of the quadrilateral is 180° then the quadrilateral is said to be cyclic