Question

Line segment AB and CD bisect each other perpendicularly at P. if PA=1.2 cm and PC=3.6 cm, then find AB+CD.

Answer 1

Answer:

AB and CD bisect each other at O i.e, AO=BO and CO=DO

in ΔCOA and ΔDOB

Given CO=OD,∠COA=∠BOD [ vertically opp angles]

AD=BD

∴ΔCOA≅ΔBOD

(i) ∴AC=BD[C.P.CT]

(ii) ∠CAB=∠ABD[C.P.CT]

again

in ΔCOB and ΔAOD

CO=OD [given]

BO=AO [given]

∠COB=∠AOD [vertically opp angles]

∴ΔCOB≅ΔAOD

∴∠CBA=∠BAD [ C.P. C.T]

(iii) and so AD∣∣CD [ ∵∠CBA=∠BAD which are altanate angles]

and AD=CB [C.P.C.T]