Question

what is op?
3
n
m
l
3
2
q
op =
submit

Explanation:

Step1: Identify triangle type

Assume △OMQ is isosceles with OM=MQ=3, OQ=2.

Step2: Find inradius formula

Inradius \( r = \frac{A}{s} \), where \( A \) is area, \( s \) semiperimeter.

Step3: Calculate semiperimeter

\( s = \frac{3+3+2}{2} = 4 \)

Step4: Calculate area via Heron's formula

\( A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{4(1)(1)(2)} = 2\sqrt{2} \)

Step5: Find inradius

\( r = \frac{2\sqrt{2}}{4} = \frac{\sqrt{2}}{2} \)? No, wait—correction: If N,P,L are tangent points, ON=OP (tangents from O to circle). Let ON=OP=x, ML=MN=3-x, PL=QL=2-x. Then ML+QL=MQ=3: \( (3-x)+(2-x)=3 \) → \( 5-2x=3 \) → \( 2x=2 \) → \( x=1 \).

Step6: Get OP value

OP=x=1.

Answer:

1