Question

I need help with these questions (see image). Please show workings.
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Answer 1

24 cm

Explanation:

The altitude from the centre to the chord is 5 cm and bisects the chord.

The radius of the circle is 26 cm ÷ 2 = 13 cm

There is a right triangle formed with legs 5 and x ( x is half the chord )

The hypotenuse is the radius, then using Pythagoras' identity

x² + 5² = 13²

x² + 25 = 169 ( subtract 25 from both sides )

x² = 144 ( take the square root of both sides )

x =
`√(144)` = 12

Then

length of chord = 2x = 2 × 12 = 24 cm

Answer 2

• 24 cm

Explanation:

The chord, if the ends connected with the center, form an isosceles triangle with two sides being a radius of the circle.

We have:

• Length of chord = x
• Height of triangle = h = 5 cm
• Radius = r = 26/2 = 13 cm

From the triangle we get:

• (x/2)² + h² = r²
• x²/4 + 5² = 13²
• x²/4 = 144
• x/2 = 12
• x = 24

The length of the chord is 24 cm