Question

Hey please write on a sheet and ans it​

Answer 1

Given that P is the mid point (since it is bisected at P) and, O is the centre. So, OP would be perpendicular to CD

'The line that joins the midpoint of a chord to the centre, is perpendicular to the chord'

i) Now, we have

OA = 15 cm

Hence, OC = 15 cm (radius of circle)

OP = 9 cm

Applying Pythagoras Theorem,

OP² + CP² = OC²

→ CP² = OC² - OP²

→ CP² = 15² - 9²

→ CP² = 225 - 81

→ CP² = 144

→ CP = √144

→ CP = 12 cm

Since P is midpoint, CD = 2CP

→ CD = 2(12)

→ CD = 24 cm

ii) Now we have to find AD

Since, OP is perpendicular, AP will also be perpendicular.

AP = OP + OA

→ AP = 9 + 15

→ AP = 24 cm

and PD = CP = 12 cm (shown above)

So, by Pythagoras Theorem

AD² = AP² + PD²

→ AD² = 24² + 12²

→ AD² = 576 + 144

→ AD² = 720

→ AD = √720

→ AD = √36 × √4 × √5

→ AD = 12√5

iii) Again, by Pythagoras Theorem,

CB² = CP² + PB²

PB = OB - OP

→ PB = 15 - 9 = 6

CB² = 12² + 6²

→ CB² = 144 + 36

→ CB² = 180

→ CB = √180

→ CB = √9 × √4 × √5

→ CB = 6√5

Answer :-

i) 24 cm

ii) 12√5 cm

iii) 6√5 cm