# Geometry

The question is to find the measure of arc PQ in Circle A. The point A is the center of the circle, and the chords PR and SQ intersect at the center. Arc PQ is (3y-10), while arc SR is (2y+20).

I know there's a theorem that states that when two chords intersect in the interior of the circle at the center, the measure of the angles are 1/2 the sum of the the two arcs.

I tried applying the theorem, but I doubt it's right because Y would equal a negative value:
1/2 * (3y-10 + 2y+20)
1/2 * (5y+10)
(2.5y+5)
-5 = 2.5y
y = -2 ?

1. 👍
2. 👎
3. 👁
1. The key point is that the two chords pass through the centre, making both of them diameters, and thus equal

since the two central angles QAP andRAS are equal, their arcs are equal
so
3y-10 = 2y+20
y = 30

then arc PQ = 3y-10 = 80

1. 👍
2. 👎

## Similar Questions

3. ### Geometry

A secant and a tangent to a circle intersect in a 42 degree angle. The two arcs of the circle intercepted by the secant and tangent have measures in a 7:3 ratio. Find the measure of the third arc. If someone could help me figure

4. ### Math

Check my answers please? There are only 10 The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X: The

1. ### pre calculus

A central angle θ in a circle of radius 8 m is subtended by an arc of length 9 m. Find the measure of θ in degrees. (Round your answer to one decimal place.) θ = ° Find the measure of θ in radians. (Round your answer to two

2. ### Geometry

Points $A$ and $B$ are on a circle centered at $O$, and point $P$ is outside the circle such that $\overline{PA}$ and $\overline{PB}$ are tangent to the circle. If $\angle OPA = 32^{\circ}$, then what is the measure of minor arc

3. ### math

Four streets enter a traffic circle at points A, B, C, and D. Name six arcs formed by the streets and the traffic circle. I only know four, and I think they are: "Arc" AB, "Arc" BC, "Arc" CD, "Arc" DA...

a) Determine the measure of the central angle that is formed by an arc length of 5 cm in a circle with a radius of 2.5cm. Express the measure in both radians and degrees, correct to one decimal place. b) Determine the arc length

1. ### math

in circle p below the lengths of the parallel chords are 20,16, and 12. Find measure of arc AB..... the chord with a length of 20 is the diameter. the chords with lengths 16 and 12 are below the diameter torwards the bottom of the

2. ### pre cal

Find the exact values for the lengths of the labeled segments a, b and p drawn in green, red, and blue, respectively. Note that r=9 is the radius of the circle, and s=8 is the arc length from the point (9,0) around the circle to

3. ### math

6. Find the z-score related to the raw score, mean, and standard deviation as follows. Assume a normal probability distribution. Raw Score50, 45, and 4.ìó=== 7. What is the Z score of a raw score 1.6 standard deviations below

4. ### Bobby

Find the length (in cm) of an arc of a circle with radius 12 cm if the arc subtends a central angle of 30°.