prove that a rectangle that circumscribed a circle is a square.

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Solution

To prove: ABCD is a square.
Proof: Tangents from external point are equal.
AP =AS --------(1)
PB =BQ --------(2)
CR =CQ --------(3)
DR =DS --------(4)
Add (1), (2), (3), (4)
AP + PB + CR + DR =AS +BQ +CQ +DS
AB +CD =BC +AD
2AB =2BC
AB =BC
So, ABCD is a square

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prove that a rectangle that circumscribed a circle is a square.

To prove: ABCD is a square. Proof: Tangents from external point are equal. AP =AS --------(1) PB =BQ --------(2) CR =CQ --------(3) DR =DS --------(4) Add (1), (2), (3), (4) AP + PB + CR + DR =AS +BQ +CQ +DS AB +CD =BC +AD 2AB =2BC AB =BC So, ABCD is a square

To prove: ABCD is a square.
Proof: Tangents from external point are equal.
AP =AS --------(1)
PB =BQ --------(2)
CR =CQ --------(3)
DR =DS --------(4)
Add (1), (2), (3), (4)
AP + PB + CR + DR =AS +BQ +CQ +DS
AB +CD =BC +AD
2AB =2BC
AB =BC
So, ABCD is a square