ABC is an inscribed triangle and chord AD bisects angle A and cuts BC at P. Prove: ADCD=ACPC.GIven: Inscribed △ABC, chord AD bisects ∠A and cuts BC at P; chord CDProve: ADCD=ACPC.Statements1.(see above)2. ∠D=∠D3.4. ∠BCD=∠DAB5.6. △ACD−△CPD7. ADCD=ACPCReasons1.Given2.3.Defintion of angle bisectors4.5.Substitution6.7.

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ABC is  an inscribed triangle and chord AD bisects angle A and cuts BC at P. Prove: ADCD=ACPC.GIven: Inscribed △ABC, chord AD bisects ∠A and cuts BC at P; chord CDProve: ADCD=ACPC.Statements1.(see above)2. ∠D=∠D3.4. ∠BCD=∠DAB5.6. △ACD−△CPD7. ADCD=ACPCReasons1.Given2.3.Defintion of angle bisectors4.5.Substitution6.7.

Nathalie Foster · Accepted Answer

Step1∠D=∠DHere angle D is equal to itself, that is reflexive property.Given, AD bisects angle A, so by definition of angle bisector∠CAD=∠DABStep2From the picture, we see that angle BCD and angle DAB are two inscribed angles with the same base points on the circle.So they are equal.∠BCD=∠DABIf we substitute angle DAB by angle BCD in∠CAD=∠DABWe get:∠BCD=∠CADSo triangle ACD and triangle CPD has two pairs of angles equal. So they are similar by AA property.Corollary 57-1 If two angles of one triangle are equal respectively to two angles of another, then the trianglesare similar. (a.a.)So,ADCD=ACPCby C.S.S.T.P, - corresponding sides of similar triangles are proportional.Answer:2) Reflexive property3) ∠CAD=∠DAB4)Inscribed angles with same base points5) ∠BCD=∠CAD6) a.a7) C.S.S.T.P.

ABC is an inscribed triangle and chord AD bisects angle A and cuts BC at P. Prove: (AD)/(CD)=(AC)/(PC). GIven: Inscribed △ ABC, chord AD bisects PSK∠ A and cuts BC at P; chord CD, Prove: (AD)/(CD)=(AC)/(PC).

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