Question

ABC is an isosceles triangle in which ab is equal to AC. P is any point in the interior of triangle ABC such that angle abc is equal to angle ACP prove that BP is equal to CP and API bisects angle BAC if u have any problem in understaning the question then see pic

Answer 1

Answer:

Step-by-step explanation:

ΔABC is an isosceles triangle AC = BC.

AP x BQ = AC²  (given)

AP x BQ = AC x AC

AP x BQ = AC x BC

AP/BC = ABQ……….(1).

Since, AC = BC

Then, ∠CAB = ∠CBA    

(angles opposite to equal sides are EQUAL)

180° – ∠CAP = 180° – ∠CBQ

∠CAP = ∠CBQ ………..(2)

In ∆APC &  ΔBCQ

AP/BC = AC/BQ [From equation 1]

∠CAP = ∠CBQ  [From equation 2]

ΔAPC∼ΔBCQ  (By SAS similarity criterion)

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