Question

In the given figure, PQ is the diameter of the circle with the center O. If PX = XS, prove that OX//QS.

Answer 1

Answer:

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Answer 2

Answer:

In the circle, PQ is the diameter. RS is a chord parallel to PQ. <ROS (O being the centre of the circle) = 40 deg.

PR and QS are produced to meet at T, then what is the measure of <PTQ?

In triangle ROS, <ROS = 40 deg, so <SRO = <RSO = (180–40)/2 = 70 deg.

<SOQ = <ROP = 70 deg.

<OSQ = <OQS = ORP = <OPR = (180–70)/2 = 55 deg.

<PTQ = 180 - 2*55 = 70 deg. Answer