Question

In the semicircle shown, the top chord is parallel to the diameter. What is its length?

• A. 5 cm
• B. 10 cm
• C. 16 cm
• D. 20 cm

Answer 1

The correct option is B

10 cm

Given RS = 1 cm

AB = 26 cm (diameter)

$\therefore$ AO = OP = 13 cm (radius)

OR = OS - SR = 13 - 1 = 12 cm

We know, in a circle, the square of half the length of a chord is the difference of the squares of the radius and the perpendicular distance of the chord from the centre of the circle.

$⟹$ PR = $\sqrt{O{P}^2-O{R}^2}$ = $\sqrt{{13}^2-{12}^2}$ = $\sqrt{169-144}$ = 5 cm

$\therefore$ PQ = 2 $\times$ PR = 2 $\times$ 5 = 10 cm