Question

Given that m∠ACB=52∘,
what is the arc length of AQB⌢?

Answer 1

To find the arc length of segment AQB⌢, we first need to find the measure of the central angle that corresponds to that arc.

Since we are given that m∠ACB = 52°, this means that the arc measure of segment ACB⌢ is also 52°.

By the Inscribed Angle Theorem, we know that the measure of the central angle is twice the measure of the inscribed angle that subtends the same arc.

So, the measure of the central angle corresponding to arc AQB⌢ is 2 * 52° = 104°.

Finally, we can use the formula for finding arc length:
Arc Length = (Central Angle Measure / 360°) * Circumference

The circumference of the circle is simply the distance around the circle, which is given by 2πr, where r is the radius of the circle.

Therefore, Arc Length of AQB⌢ = (104° / 360°) * 2πr
Arc Length of AQB⌢ = (26/90) * 2πr
Arc Length of AQB⌢ = (13/45) * 2πr
Arc Length of AQB⌢ = (26πr) / 45

So, the arc length of AQB⌢ is (26πr) / 45.