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Giải bài tập 6 trang 82 SGK Toán 9 tập 1 - Chân trời sáng tạo

Cho hai đường tròn (A; 6 cm) và (B; 4 cm) cắt nhau tại C, D, AB = 8 cm. Gọi I, K lần lượt là giao điểm của hai đường tròn đã cho với đoạn thẳng AB (Hình 21). a) Tính độ dài của các đoạn thẳng CA, CB, DA và DB. b) Điểm I có phải là trung điểm của đoạn thẳng AB không? c) Tính độ dài của đoạn thẳng IK.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Cho hai đường tròn (A; 6 cm) và (B; 4 cm) cắt nhau tại C, D, AB = 8 cm. Gọi I, K lần lượt là giao điểm của hai đường tròn đã cho với ▨đoạn thẳng AB (Hình 21).

a) Tính độ dài của các đoạn thẳng CAꦕ, CB, DA và DB.

b) Điểm I có phải là trung điểm của đoạn thẳng AB 💜không?

c) Tính độ dài của đoạn thẳng IK.

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Đọc kĩ dữ liệu đề bài để vẽ hình

- Dựa🍷 vào khoảng cách từ tâm tới các điểm nằm trên đường tròn để 💃xác định khoảng cách.

- Chứng minh I nằm giữa AB và khoảng cáchꦑ IA = IB nên I là trung điểm của AB.

- Chứng minh I nằm giữa AK và AI + IK = AK rồi suy ra khoảng cách IK.

Lời giải chi tiết

a) Hai điểm C꧋ và D nằm trên đường tròn (A; 6 cm) nên CA 🧔= DA = 6 cm.

Hai điểm C và D nằm trên đườ🧜ng tròn ༺(B; 4 cm) nên CB = DB = 4 cm.

b) Trên tia BA có BI = 4 cm; AB = 8 cm

nên BI < AB suy ra I nằm giữa A và B (1)

Su♛y ra AI + IB =ꦐ AB nên AI = AB – IB = 8 – 4 = 4 cm

Do đó: AI = BI (= 4 cm) (2)

Từ (1) và (2) suy ra I là trung điểm của AB

c) Trên tia AB có AI = 4 cm; AK = 6 cm

Vì AI < AK nên điểm I nằm giữa A và K

Suy ra AI + IK = AK

Suy ra IK = AK – AI = 6 – 4 = 2 cm.

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