Problems Related to Theorem of Thabit ibn Qurra

See figure below

Conditions:

• m ∠APC = m ∠BQC = m ∠ACB
• Sa, Sb, and Sc are squares on BC, AC, and AB respectively
• |AB| = c, |BC| = a, |CA| = b, and |PC| = d

Problems

1. Prove that : area Sb = area Rb and area Sa = area Ra
2. Prove that ab = cd