Debanjan drew a line segment PQ of which mid-point is R and two circles are drawn with PR adn PQ as diameter . Deberatee drew a straight line through the point which interects the first circle at the point S and the second circle at the point T. Prove that PS=ST

Explanation

Let O be the centre of the circle drawn with PR as the diameter.
Let us join S,R and T,R Since PR is a diameter `:. anglePSR=90^(@) [ :.` Semicircular angle]
Obviouslyl. `angleTSR=90^(@)`[ Sinnce PST is a striaght line, so that `anglePST=1` striaght line `=180^(@)`]
Now in `Delta PSR and Delta TSR, PR=TR [ :. ` radii of same circle with centre At R]
`anglePSR= angleTSR[ :.` each is right angle] and SR is common to both.
`:. Delta PSR~=Delta TSR` [ by teh R-H-S condition of congruency]
`:. PS=ST [ :.` similar side of two congruent tirangles]
Hence, `PS=ST`