PQ and RS are two chords of a circle with centre O intersecting each other. if X is any points on chord RS such that XO//SQ prove that PX=SX
Answers
Answered by
1
Thus we have OP = OQ which is PX=SX
Step-by-step explanation:
- When the chords PR and QS are extended to meet at an external common point(O), then the following property always holds good.
- OP x OR = OQ x OS
- Also, this theorem gives way to the better known fact that 2 tangents form a common external point to a circle of the same length
- Back to the problem :
- From F.S 1, we know that in similar triangles OPQ and OPS, OP / OR = OQ / OS.
- Multiplying the above equation with the first equation, we get: (OP^2 = OQ^2 to OP = OQ). Sufficient.
- From F.S 2, we know that PR = QS.
- Thus, (OP x (OP+PR) = OQ x (OQ + QS) = OP^2 - OQ^2 + PR(OP - OQ) = 0
- Thus, (OP - OQ)(OP + OQ + PR) = 0
- As distance can never be negative, we have OP = OQ. Sufficient.
Similar questions