The length of the chord CE is 24.46 in
To find the length of the chord CE, we solve the question using pythagoras' theorem
What is a chord?
A chord is a line segment touching two points in a circle.
What is pythagoras' theorem?
Pythagoras' theorem states that in any right angled triangle with sides a, b and c where c is the hypotenuse side, we have that
c² = a² + b²
The required triangle
Now form the diagram the radius of the circle BE forms a right angled triangle with the perpendicular to the chord, BO and the midway between the chord, OE.
BO = BD - OD
= 20 in - 5 in
= 15 in
From pythagoras,
BE² = DE² + BO²
making DE subject of the formula, we have
DE = √(BE² - BO²)
DE = √((20 in)² - (15 in)²)
DE = √(400 in² - 225 in²)
DE = √(175 in²)
DE = 13.23 cm
The length of the chord
Since the chord CE = 2DE,
So, CE = 2 × 13.23 in
= 26.46 in
So, the length of the chord CE is 24.46 in
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