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Prove that riangle DSF extrm is similar to riangle OHG

May 22, 2026Mathematics

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Step-by-step solution

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Here's the solution to your Euclidean geometry problem:

Part 7.1: Prove that $\triangle DSF \parallel\parallel \triangle OHG$

To prove that two triangles are similar, we need to show that two pairs of corresponding angles are equal (AA similarity).

Identify equal angles in $\triangle DSF$ .
DF and DS are tangents from an external point D to the circle.
Therefore, $DF = DS$ (tangents from common external point).
Since $DF = DS$ , $\triangle DSF$ is an isosceles triangle.
Thus, $\angle DSF = \angle DFS$ (angles opposite equal sides).
Identify

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