Multiple choice

From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA $=$ 10 cm, find the the perimeter of the $ \Delta PCD$.

  1. 10 cm

  2. 15 cm

  3. 20 cm

  4. 25 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Tangents from an external point to a circle are equal. PA = PB = 10. Also, CA = CE and DB = DE. Perimeter of triangle PCD = PC + CD + DP = PC + (CE + ED) + DP = (PC + CA) + (DB + DP) = PA + PB = 10 + 10 = 20.

AI explanation

Because tangents from a common external point are equal, AC equals CE and DE equals DB. The perimeter of triangle PCD is PC plus CD plus PD, which can be rewritten by replacing CD with CE plus ED as PC plus CE plus ED plus PD. Substituting CE with CA and ED with DB gives PC plus CA plus DB plus PD, simplifying to PA plus PB. Since PA equals 10 cm, PA plus PB is 20 cm, so the perimeter is 20 cm.

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