Question

If line segment BH = 3, line segment BF = 10, line segment GH= 2, find HD 15 11 10.5 ?

Answer 1

HD = 10.5

Given BH = 3, GH = 2, BF = 10

Step 1: To find HF:

HF = BF – BH

HF = 10 – 3

HF = 7

Step 2: To find HD:

We know that if two chords intersects inside a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

⇒ GH × HD = BH × HF

⇒ 2 × HD = 3 × 7

⇒ HD = 10.5

HD = 10.5.

Answer 2

HD = 10.5

Explanation:

Given BH = 3, GH = 2, BF = 10

Step 1: To find HF:

HF = BF – BH

HF = 10 – 3

HF = 7

Step 2: To find HD:

We know that if two chords intersects inside a circle, the product of the lengths of the segments of one chord equals the product of the lengths of the segments of the other chord.

⇒ GH × HD = BH × HF

⇒ 2 × HD = 3 × 7

⇒ HD = 10.5

Hence, the value of HD = 10.5.