The length of the diameter of a circle with its centre at O is 26 cm. The distance of the chord PQ form the point O is 5 cm . Calculate the length of th chord PQ.

Explanation

Let ` OD bot PQ therefore D` is the mid -point
`i.e., PD = (1)/(2) PQ or , PQ = 2PD`
`because OD bot PQ, therefore ` distance of PQ form O = OD = 5 cm
Now diameter of the circle = 26 cm
`therefore ` Radius ` = (26)/(2) cm = 13 cm`
Also , in right -angled triangle OPD we get,
` OP^(2) = OD^(2) + PD^(2)`
or `(13)^(2) = (5)^(2) = PD^(2) or 169, = 25 + PD^(2)`
or ` PD^(2) = 169 - 25 = 144 rArr PD = sqrt(144) = 12`
`therefore PQ = 2PD = 2 xx 12 cm = 24 cm `
` therefore ` lenght of the chord PQ = 24 cm