SAT Math Practice Question #2538 (Medium) | Test Citadel
TC
Test Citadel
SAT Math Difficulty: Medium

Digital SAT Math Practice Question #2538

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

The circle $(x - 1)^2 + (y + 3)^2 = r^2$ is tangent to the $x$-axis. What is the value of $r$?
Select Your Answer:
Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
⚡ 15-Second Desmos Speed Hack

Geometry & Trig Rule: Always sketch the triangle or circle and check for standard Pythagorean triples (3-4-5, 5-12-13, 7-24-25, 8-15-17).

Masterclass Solution & Distractor Trap Analysis

The center is $(1, -3)$. Distance from the center to the $x$-axis ($y = 0$) is $|-3| = 3$. For tangency, $r = 3$....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

🔒 Citadel Pro Scholar Vault

Unlock Full Solution & 2,600+ Official Drills

Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.

Socratic Assistant

Targeted hints without disclosing final solutions.

I am your Socratic tutor. Click one of the quick guidance buttons above or ask a specific question below about a formula or method.