Question

Point P lies on circle C, x^2+y^2=36. There are two unique tangents to circle D, x^2+y^2=18 that pass through point p. What is the measure of the angle between the two tangent lines?

Answer 1

• 90°

Explanation:

Refer to attached

Red circle is C with radius 6 and green circle is D with radius √18.

PM and PN are tangents to circle D.

M and N are right angles as tangents are perpendicular to radius.

We need to find the measure of ∠MPN.

We'll work out this angle using trigonometry:

• OM / OP = sin (∠MPO)
• sin (∠MPO) = √18/6 = √2/2
• m∠MPO = arcsin ( √2/2) = 45°

∠NPO is same as ∠MPO, therefore:

• m∠MPN = 45°*2 = 90°