# two chords intersect at a point inside a circle that is not the center of the circle. which statement must be true? the measures of each pair of opposite arcs sum to 180°. each angle measure is equal to the measure of the arc it intercepts. the sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs. each arc measure is equal to one-half the sum of the vertical angles that intercept the arc.

### James

Guys, does anyone know the answer?

get two chords intersect at a point inside a circle that is not the center of the circle. which statement must be true? the measures of each pair of opposite arcs sum to 180°. each angle measure is equal to the measure of the arc it intercepts. the sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs. each arc measure is equal to one-half the sum of the vertical angles that intercept the arc. from EN Bilgi.

## Two chords intersect at a point inside a circle th

Answer: .

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## Two chords intersect at a point inside a circle that is not the center of the circle. Which statement must be true? The measures of each pair of opposite arcs sum to 180 ° Each angle measure is equal to the measure of the arc it intercepts. The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs. Each arc measure is equal to one-half the sum of the vertical angles that intercept the arc

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### Gauthmathier3302

Grade 10 · 2021-06-25

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Two chords intersect at a point inside a circle that is not the center of the circle. Which statement must be true?

The measures of each pair of opposite arcs sum to

Each angle measure is equal to the measure of the arc it intercepts.

The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs.

Each arc measure is equal to one-half the sum of the vertical angles that intercept the arc

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### Gauthmathier6284

Grade 10 · 2021-06-25

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## Unit test review Flashcards

Study with Quizlet and memorize flashcards terms like Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2. Which circle could represent the base of the vase? Use 3.14 for ., Triangle BCD is isosceles and BC ≅ BD. What is the measure of BC, A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. Each of the central angles has a measure of 40°. How many sides does the polygon have? and more.

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Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2.

Which circle could represent the base of the vase? Use 3.14 for .

Click card to see definition 👆

B

Click again to see term 👆

Triangle BCD is isosceles and BC ≅ BD.

What is the measure of BC

Click card to see definition 👆

130

Click again to see term 👆

1/15 Created by theanswers1234

### Terms in this set (15)

Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2.

Which circle could represent the base of the vase? Use 3.14 for .

B

Triangle BCD is isosceles and BC ≅ BD.

What is the measure of BC

130

A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. Each of the central angles has a measure of 40°. How many sides does the polygon have?

9

In the diagram of circle O, what is the measure of ∠ABC?

34

Angle G is a circumscribed angle of circle E.

What is the measure of angle G, in terms of x?

x° + x°

Which equation represents the general form a circle with a center at (-2, -3) and a diameter of 8 units?

x2 + y2 + 4x + 6y - 3 = 0

What is the radius of a circle whose equation is (x - 7)2 + (y - 10)2 = 4?

2 units

UV and RV are secant segments that intersect at point V.

What is the length of TV?

3 units

Given: Circle O; intercepts ; D intercepts

Prove:

Two statements are missing reasons. What reason can be used to justify both statements 2 and 3?

inscribed angles theorem

Which circle shows that measures 60°?

C

The chords intersect at point U.

What is the value of y?

6

In circle Y, what is m?

82

Line segment BD passes through the center of circle C, BH = a, and HD = 8.

What is the length of the diameter?

12.5

Two chords intersect at a point inside a circle that is not the center of the circle. Which statement must be true?

The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs.

A circular table top has a radius of 24 inches.

What is the area of the table top, to the nearest square inch? Use 3.14 for .

1809

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## Angle of Intersecting Chords Theorem

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## Angles of Intersecting Chords Theorem

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

In the circle, the two chords

PR ¯ ¯ ¯ ¯ ¯ PR¯ and QS ¯ ¯ ¯ ¯ ¯ QS¯

intersect inside the circle.

m∠1= 1 2 (m PQ +m RS ) m∠1=12(mPQ⌢+mRS⌢) and m∠2= 1 2 (m QR +m PS ) m∠2=12(mQR⌢+mPS⌢)

Since vertical angles are congruent,

m∠1=m∠3 m∠1=m∠3 and m∠2=m∠4 m∠2=m∠4 .

**Example:**

In the circle shown, if

m PQ =92° mPQ⌢=92° and m RS =110° mRS⌢=110° , then find m∠3 m∠3 . Substitute. m∠3= 1 2 (m PQ +m RS ) = 1 2 (92°+110°) = 1 2 (202°) =101°

m∠3=12(mPQ⌢+mRS⌢) =12(92°+110°) =12(202°) =101°

Therefore, m∠3=101° m∠3=101° .

Guys, does anyone know the answer?