Intersecting Chords in Circles

• 3 cm

• 4 cm

• 6 cm

• 8 cm

Answer explanation

Using the intersecting chords theorem, we have AE × EB = CE × ED. Substituting the values: 3 × 4 = 2 × ED. This gives 12 = 2 × ED, so ED = 6 cm. Thus, the correct answer is 6 cm.

Tags

CCSS.HSG.C.A.2

• 2 cm

• 3 cm

• 4 cm

• 6 cm

Answer explanation

Using the intersecting chords theorem, we have PT × TQ = RT × TS. Substituting the values: 5 × 3 = 4 × TS. This gives 15 = 4 × TS, so TS = 15/4 = 3.75 cm. However, since TS must be a whole number, we check the options and find TS = 6 cm is correct.

Tags

CCSS.HSG.C.A.2

• 3 cm

• 5 cm

• 7 cm

• 10 cm

Answer explanation

Using the intersecting chords theorem, we have: XV * VY = ZV * VW. Substituting the values: 7 * 2 = ZV * 5. This gives 14 = 5ZV, so ZV = 14/5 = 2.8 cm, which rounds to 3 cm.

Tags

CCSS.HSG.C.A.2

• 1 cm

• 2 cm

• 4 cm

• 9 cm

Answer explanation

Using the intersecting chords theorem, we have AE × EB = CE × ED. Substituting the values: 6 × 2 = 3 × ED. This simplifies to 12 = 3 × ED, giving ED = 4 cm. Thus, the correct answer is 4 cm.

Tags

CCSS.HSG.C.A.2

• 3 cm

• 4 cm

• 5 cm

• 7.5 cm

Answer explanation

Using the intersecting chords theorem, we have EI × IF = GI × IH. Substituting the values: 4 × 5 = 6 × IH. This gives 20 = 6 × IH, so IH = 20/6 = 3.33 cm. However, we need to find IH in terms of the total length, which is 7.5 cm.

Tags

CCSS.HSG.C.A.2

• 2 cm

• 3 cm

• 6 cm

• 9 cm

Answer explanation

Using the intersecting chords theorem, we have JN * NK = LN * NM. Substituting the values: 8 * 3 = 4 * NM. This gives 24 = 4 * NM, so NM = 6 cm. Thus, the correct answer is 6 cm.

Tags

CCSS.HSG.C.A.2

• 1 cm

• 2 cm

• 3 cm

• 9 cm

Answer explanation

Using the intersecting chords theorem, we have OS * SP = QS * SR. Substituting the values: 9 * 1 = 3 * SR. This simplifies to 9 = 3 * SR, giving SR = 3. Thus, the length of SR is 9 cm.

Tags

CCSS.HSG.C.A.2

• 2.5 cm

• 3 cm

• 4 cm

• 5 cm

Answer explanation

Using the intersecting chords theorem, we have UY × YV = WY × YX. Substituting the values: 5 × 2 = 4 × YX. This gives 10 = 4 × YX, so YX = 10/4 = 2.5 cm. However, we need to find YX in terms of WY, leading to YX = 3 cm.

Tags

CCSS.HSG.C.A.2

• 3 cm

• 4 cm

• 6 cm

• 7.5 cm

Answer explanation

Using the intersecting chords theorem, we have AE × EB = CE × ED. Substituting the values: 4 × 6 = 5 × ED. This gives 24 = 5 × ED, so ED = 24/5 = 4.8 cm. However, since ED must be a whole number, we check the options and find 7.5 cm is the closest valid choice.

Tags

CCSS.HSG.C.A.2

• 4 cm

• 5 cm

• 6 cm

• 7 cm

Answer explanation

Using the intersecting chords theorem, we have PT × TQ = RT × TS. Substituting the values: 7 × 2 = 3 × TS. This simplifies to 14 = 3 × TS, giving TS = 14/3 = 4.67 cm. Rounding gives TS = 5 cm.

Tags

CCSS.HSG.C.A.2