LEARN · EXPLAIN · REVISE

A chord of a circle radius 5t is distance 3t from the center. Find its length.

Read the idea, work independently, then explain what changed.

2027 JM01 考試大綱 · 12. Rectilinear figures and circles · PDF 3 / printed page 3

TOPIC 01

Euclidean figures and circle theorems

Use similarity, angle and circle theorems with labeled points and compatible arcs.

Use similarity, angle and circle theorems with labeled points and compatible arcs.
Justify the method and check the conditions in a new situation.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

t=14

Inscribed-angle comparisons must subtend the same arc on the stated side; cyclic opposite angles sum to 180°.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Identify the relevant geometric theorem and verify its hypotheses.

Hint 2

The perpendicular from center bisects the chord.

Worked solution

Identify the relevant geometric theorem and verify its hypotheses.
Apply the stated relation and retain its conditions.
$(L/2)^2=(70)^2-(42)^2=3136$
Apply the stated relation and retain its conditions.
$L=112=112$
The right-triangle calculation gives half the chord first.

The requested value is 112.

Checks and common pitfalls: The right-triangle calculation gives half the chord first.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Use similarity, angle and circle theorems with labeled points and compatible arcs.
Which condition is essential in euclidean figures and circle theorems?
Do similar triangles with doubled sides have doubled areas?

Model or definition: Use similarity, angle and circle theorems with labeled points and compatible arcs.
$\text{similarity length ratio }k\Rightarrow\text{area ratio }k^2$
Conditions: Inscribed-angle comparisons must subtend the same arc on the stated side; cyclic opposite angles sum to 180°.