circle 點計??

第一幅圖(Example 2):

AO = CO = BO (radius)
∠CAO = ∠ACO (base∠s, isos.△)
∠BOP = ∠CAO = ∠ACO (corr.∠s,AC parallel OP)
∠BOP = ∠CAO = ∠ACO = ∠COP (alt.∠s,AC parallel OP)
OP = OP (common ∠)
∴△COP congruent △BOP

∠OBP = ∠OCP = 90° (corr.∠s, congruent △s)
∴CP is a tangent to the circle (converse of tangent ⊥ radius)


第二幅圖(mc):

3. Consider the larger circle, SP = SR (tangent from ext. pt.)
Consider the smaller circle, SP = SQ (tangent from ext. pt.)
SQ = SP = SR

∠SPQ + ∠SQP + 38° = 180° (∠sum of △)
2∠SQP = 142° (base ∠s, isos.△)
∠SQP = 71°

∠SQR + ∠SRQ + 16° = 180° (∠sum of △)
2∠SQR = 164° (base ∠s, isos.△)
∠SQR = 82°

∴∠PQR = ∠SQP + ∠SQR = 71° + 82° = 153°

6. Consider △ACD, ∠CAD = ∠DCS = 39° (∠ in alt. seg)
Consider △ABD, ∠ADB = ∠BAP = 47° (∠ in alt. seg)
∠AKD + ∠CAD + ∠ADB = 180° (∠ sum of △)
∠AKD + 39° + 47° = 180°
∠AKD = 94°