Question

Prove thaPQ=RS.PQRS is a line segment which cuts 2 Circles and passes through mid point M of OC.

Answer 1

Answer:

Step-by-step explanation:

In ΔMAO & ΔMBC,

OM=MC(as M is the mid-point of OC, given)

∠OMA=∠BMC(Vertically opposite angles are always equal)

∠OAM=∠MBC=90°(each 90°)

∴ΔOMA≅ΔMCB (A.S.A criteria of congruenceΔ)

⇒OA=BC(C.P.C.T)

Also, OM=MC(given), from this, we can conclude that both circles have equal radius and thus congruent.

PQ & RS are of two congruent circle which are equidistant from centre(as OA=BC)

⇒RS=PQ(Two chords of a congruent circle which are equidistant from its center must have the same length.)