From an external point P, two tangents touch a circle at A and B, and PA = 15 cm. A third tangent touches the circle at a point Q on the arc between A and B, meeting PA at C and PB at D. What is the perimeter of triangle PCD?

Question

Accepted Answer

30 cm. Equal tangents give CQ = CA and DQ = DB. So the perimeter PC + CD + DP = PC + (CQ + QD) + DP = PC + CA + DB + DP = PA + PB. Since PB = PA = 15 cm, the perimeter is 30 cm — it does not depend on where Q is chosen.

From an external point P, two tangents touch a circle at A and B, and PA = 15 cm. A third tangent touches the circle at a point Q on the arc between A and B, meeting PA at C and PB at D. What is the perimeter of triangle PCD?

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Geometry practice