Question

please answer the question to get 30 points​

Answer 1

There you go
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Answer 2

Step-by-step explanation:

From figure:

Let l₁ and l₂ be the two intersecting lines.

Let a circle with centre O touches the two lines l₁ and l₂.

In ΔOAP and ΔOBP, we have

⇒ OA = OB

⇒ PA = PB

⇒ OP = OP

By SSS-congruence criterion, we have

⇒ ΔOAP ≅ ΔOBP

⇒ ∠APO = ∠BPO

⇒ OP is the bisector of ∠APB

⇒ O lies on the bisector of the angle between l₁ and l₂.

Hence, locus of centres of circles which touch two intersecting lines is the pair of angle bisectors between the two lines.

Hope it helps!