Question

B is 34 mm from the center of circle O, which has radius 16 mm. BP and BR are tangent segments. AC is tangent to O at point Q. Find the perimeter of ABC?

Answer 1

56.72mm

Explanation:

BQ = 34 - 16 = 18mm

Using similar triangle,

AQ = QC =(16*18)/34 = 8.47mm

AC = 2*8.47 = 16.94 mm

Since

BC = AB = sqrt( AQ² + BQ²)

BC = AB = sqrt( 8.47² + 18²)

BC = AB = 19.89mm

Perimeter of triangle ABC = AB + BC + AC

P = 19.89 + 19.89 + 16.94

Perimeter = 56.72mm