In the circle of adjoining figure with its centre at ` O , OP bot AB,` if AB = 6 cm and PC = 2 cm the find the length of radius of the circle .

Explanation

Let us join O, A . The the radius of the cirle is OA. Now AB = 6 cm,
`therefore AP = (1)/(2)AB `, [ because ` P is mid - point of AB]`
or ` , AP = (1)/(2) xx 6 cm , therefore AP = 3 cm ………..(1)`
Again , in the right - angled triangle ` AOP , OA^(2) = AP^(2) = OP^(2)`
` or OA^(2) = (3)^(2) + ( OC - 2)^(2) [ because OP = OC - 2]`
` or , OA^(2) = (3)^(2) + (OC - 2)^(2) [ because OP = OC - 2]`
` or , OA^(2) = 9 = OC^(2) - 4 OC + 4 or , OA^(2) = 13 + OA^(2) - 4 OC`
` or 0 = 13 - 4 OC or 4 OC = 13`
` or OC = (13)/(4) = 3.25`
Hence the radius = 3.25 cm .