Clarity amidst chaos

Kamsi heaved a deep sigh as she stepped into the classroom, the weight of the retest pressing down on her. The air felt thick with the remnants of anxiety from the last time she faced this challenge.

"Good morning, Mr. Felix," she greeted, offering a slight bow, her hands fidgeting at her sides.

"Morning, Ms. Chibuike. How was your night?" Mr. Felix asked, a genuine smile spreading across his face.

Kamsi raised an eyebrow, taken aback by the warmth of his question. It was unusual for a teacher to inquire about her well-being. "It was lovely," she replied, forcing a polite smile as she decided to return the question. "And yours?"

Mr. Felix blinked, momentarily surprised. "Sorry…" he started, but Kamsi's instinctive worry made her tense. Had she overstepped?

"It was stressful," he continued, breaking into a grin. "I spent all night compiling today's test questions for you."

Kamsi's stomach sank, a flicker of guilt crossing her features. "I'm sorry—"

"Just kidding!" he laughed, his voice ringing with lightheartedness. Kamsi let out a nervous chuckle, her shoulders relaxing slightly.

"Look at you, so easy to rattle," he teased, leaning against his desk, his devilish smile flickering as he added, "My night was lovely; my wife made sure of it." He leaned forward, eyes twinkling with mischief. "If you know what I mean."

Kamsi's brows creased in confusion, her cheeks warming at the implication. Shameless! She thought, glancing away, wondering if all teachers were like this or just him. Mr. Felix noticed her discomfort and couldn't help but chuckle again. "Gotcha!" he exclaimed, his laughter filling the room, and Kamsi's mouth fell open in shock. Was he serious?

"I'm not married... yet," he added, raising his fingers in mock solemnity. "See?"

"Okay…" she muttered, half-amused, half-embarrassed.

"I just wanted to help relieve some of the tension I sense around you," he said, his tone turning sincere. "It's never good to walk into an exam feeling like you're about to be interrogated." He gestured to her anxious expression, his eyes kind but piercing. "That anxiety can mess with your memory and make you forget everything you studied."

Kamsi sighed, her gaze dropping to the floor. "I can't help it," she murmured, feeling the weight of her inadequacy.

"Yes, you can! All you have to do is relax," he encouraged, poking his temples for emphasis. "Focus less on the exam and more on what's in here." He tapped his head. "It will help if you don't dive right into the questions. Take a moment to breathe before you start answering."

"But what if I don't have enough time?" she asked, her voice barely above a whisper, worry lacing her tone.

"That's where time management comes in. Skim through the questions first. Spot the ones you know," he advised, his confidence reassuring. "Answer those first—don't waste precious minutes on what you don't know when you can use that time to tackle the easier ones."

Kamsi nodded, absorbing his words as if they were a lifeline. "Okay," she said softly, the knot in her stomach loosening just a bit.

"And lastly," he added, leaning closer, his expression serious but warm, "make sure to give it your all, but don't overpressure yourself, alright?"

"Thank you, Mr. Felix," she said, genuine gratitude in her eyes.

"It's okay," he replied, his voice softer now. Leaning forward again, he lowered his voice to a conspiratorial whisper. "If you find yourself stumped on a question, you can always ask me for help. After all, we're the only ones here," he added, shrugging playfully with a grin that felt oddly reassuring.

Kamsi stared at him for a moment, then let out a laugh, the tension in her shoulders finally melting away. "You almost got me this time."

"Much better!" he said, referring to her brightening mood. "Now, take a seat."

Kamsi settled into the chair at the front of the room, the familiar scent of chalk and paper surrounding her. As Mr. Felix distributed the test sheets, she felt a flicker of determination.

"You've got an hour and thirty minutes to finish. Your time starts now." He pressed the timer, then took his own seat, observing her closely.

Kamsi stared at the blank page for a moment, her heart racing. She picked up her pen, ready to write, but then, recalling his advice, she hesitated. Taking a deep breath, she skimmed through the questions instead, feeling a small smile tug at her lips as she recognized the familiar ones.

Mr. Felix's smile widened, pride evident in his gaze as he picked up a book to read, glancing over the rim at her with encouragement.

Going through the questions, Kamsi couldn't help but smile internally as she recognized several of them. Confidence surged within her as she tackled the familiar ones first, skipping the more challenging problems. After finishing the ones she felt secure about, she circled back to the ones that stumped her, her mind racing to recall formulas and concepts.

As she mulled over a particularly tricky question, her thoughts drifted to Xavier. She remembered how he had helped her with similar problems, his tone both teasing and instructive as he guided her through the concepts.

"Alright, let's break it down," Xavier had said, leaning back in his chair, his arms crossed as he explained the problem with a devilish grin. "In triangle ABC, you've got angle BAC as 30 degrees and angle ABC as 60 degrees. The side AB is 10 cm, and point D lies on BC, right?"

Kamsi had nodded, her brow furrowed in concentration.

"First off, you need to know that since you have a 30-60-90 triangle, you can find AC using the ratio of the sides," he continued, his voice confident and steady. "So, AC is going to be AB times the square root of three. That's 10√3 cm. Got it?"

She nodded again, remembering how the formula had clicked into place with his help.

"Now for the angle bisector theorem," he had added, leaning forward as if the weight of the world was on this simple theorem. "It states that BD/DC = AB/AC. So, if you plug in the numbers, it's 10 over 10√3, which simplifies to 1/√3. Easy, right?"

Kamsi had smiled, his enthusiasm infectious.

"Then you know BD + DC equals BC, and since AB is 10 cm, you can solve for DC by rearranging the equation. So, DC = 10 - (10/√3). That gives you DC = 10(1 - 1/√3)."

She could still hear his playful tone as he had rationalized the denominator, saying, "Now make sure to finish it! You don't want to leave it hanging. DC = 10(√3 - 1)/√3. That's approximately 5.88 cm. Simple geometry, Kamsi!"

Shaking her head at the memory, she recalled how his confidence had lifted her spirits. She wrote down her thoughts quickly, feeling the solution crystallizing in her mind:

Final answer CD = 10(√3 - 1)/√3 ≈ 5.88 cm.

Kamsi's heart raced as she moved to the next question, feeling a renewed sense of determination. With Xavier's words echoing in her mind, she was ready to tackle anything that came her way.