Question

OR
In Figure-6, find the perimeter of A ABC, if AP = 12 cm.
BD
Figure-6​

Answer 1

Answer:

AP=AB+BP

(BP=BD)

So ,

AP=AB+BD

similarly....AQ=AC+CD

Perimeter of ABC=AP+AQ

=12+12 (AP=AQ)

Perimeter of ABC=24 cm

Answer 2

Perimeter of the triangle ABC is 24 cm.

Step-by-step explanation:

Perimeter of ΔABC = AB + BC + CA

Since AP = AB + BP ⇒ AB = AP - BP

and AQ = AC + CQ ⇒ AC = AQ - CQ

Now perimeter of ΔABC = (AP - BP) + BC + (AQ - CQ)

                                        = AP + AQ + BC - (BP + CQ)

                                        = AP + AQ + BC - (BD + CD)

[ BP ≅ BD, since BP and BD are the tangents from B to the circle]

[Similarly, CD ≅ CQ, as CD and CQ are the tangents from the point C to the  circle]

Now perimeter = AP + PQ + BC - BC

                          = 12 + 12

                          = 24 cm

Therefore, perimeter of the triangle ABC is 24 cm.

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