Question

two circles with Centre M and n intersect each other at p and q ​

Answer 1

Answer:

So what u need write it properly.

Answer 2

Answer:

We join MN.

As PRMN is a cyclic quadrilateral,

∠R + ∠PNM = 180° …………………..(1) (opposite angles of a cyclic quadrilateral)

Also, QSMN is a cyclic quadrilateral,

∠S + ∠ QNM = 180° ……………………(2) (opposite angles of a cyclic quadrilateral)

Adding (1) and (2)

∠ R + ∠S + ∠ PNM + ∠QNM = 360°

⇒ ∠ R + ∠S + 180 = 360 (PQ is a straight line)

⇒ ∠ R + ∠S = 180°

Similarly we have,

As PRMN is a cyclic quadrilateral,

∠P + ∠RMN = 180° …………………..(3) (opposite angles of a cyclic quadrilateral)

Also, QSMN is a cyclic quadrilateral,

∠Q + ∠ SMN = 180° ……………………(4) (opposite angles of a cyclic quadrilateral)

Adding (3) and (4)

∠ P + ∠Q + ∠ RMN + ∠SMN = 360°

⇒ ∠ P + ∠Q + 180 = 360 (RS is a straight line)

⇒ ∠ P + ∠Q = 180°

Therefore, PR ∥ SQ.

Step-by-step explanation:

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