Q4 of 26 Page 86

In the figure 6.19, C is the center of the circle. seg QT is a diameter CT = 13, CP = 5, find the length of chord RS.


We join C to S to form ΔCPS.

CP = 5 (given)


Radius of circle = CT = 13 (given)


Therefore CS = 13 (radius of the same circle)


In ΔCPS,


⇒ CS2 = CP2 + PS2


⇒ 132 = 52 + PS2


⇒ PS2 = 169-25


⇒ PS2 = 144


⇒ PS = 12 units


We know that a perpendicular drawn from the center of a circle on its chord bisects


the chord.


PS = RP = 12 units


RS = 2×PS = 2×12 = 24 units


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