Question

Given: segments PC and GN intersect each other at O.
OP × OC = ON × OG

Prove that: angle P = angleN
and angle C = angle G​

Answer 1

Answer:

Consider ∆ POG and ∆ NOC

Given

$\frac{op}{on} = \frac{on}{oc}$

By basic proportionality theorem ∆ POG and ∆ NOC are similar.

in similar triangles corresponding angles of each triangles are equal to the angles of other triangle.

<NOC = <POG

and angle P = angle N

also angle G = angle c