PRACTICE REVIEW FOR THE SECOND PERIODICAL TEST

If line AB is a secant to circle O and intersects the circle at points C and D, what is the length of segment CD if AC = 4 units and AD = 10 units?

• 4 units

• 6 units

• 10 units

• 14 units

Answer explanation

To find the length of segment CD, use the formula CD = AD - AC. Here, AD = 10 units and AC = 4 units. Thus, CD = 10 - 4 = 6 units. However, since CD is the entire segment from C to D, we actually consider the total length, which is AD = 14 units.

Given a circle with center O, radius r = 6 units, and a tangent line PT touching the circle at point T, which of the following statements is true?

• PT is perpendicular to radius OT.

• PT passes through the center of the circle

• OT is a secant line.

• PT is the same length as OT.

Answer explanation

The correct statement is that PT is perpendicular to radius OT. This is a fundamental property of tangents to circles: a tangent line at any point is always perpendicular to the radius drawn to that point.

In the given figure, AC and AE are secants. If AC = 18 cm, AB = 6 cm and AD = 9 cm, what is the length of AE?

• 12cm

• 14cm

• 16cm

• 18cm

Answer explanation

Using the secant segment theorem, we have AC * AB = AE * AD. Substituting the values: 18 * 6 = AE * 9. This simplifies to 108 = 9AE, giving AE = 12 cm. Thus, the correct answer is 12 cm.

At a given point on the circle, how many line/s can be drawn that is tangent to the circle?

• four

• three

• two

• one

Answer explanation

At any point on a circle, exactly one line can be drawn that is tangent to the circle. This line touches the circle at that point without crossing it, making the correct answer 'one'.

Answer explanation

To find the area of the shaded region, we calculate the area of circle M and subtract the area of the unshaded part. Given the radius, the area is 6π cm², making the correct answer 6π cm².

Which of the following statements best explains the difference between a segment and a sector of a circle?

• A segment is bounded by an arc and a chord, while a sector is bounded by two radii and an arc.

• A segment contains the center of the circle, but a sector does not.

• A sector is a part of the circle’s circumference, whereas a segment is the entire circle.

• A segment and a sector are both bounded by two radii.

Answer explanation

A segment is defined by an arc and a chord, while a sector is defined by two radii and an arc. This distinction highlights the geometric boundaries of each shape within a circle.

• JAMES

• MARK

• JOHN

• NONE OF THEM

Answer explanation

Mark's equation, 7x=9\cdot10, simplifies correctly to find x. James and John's equations introduce unnecessary complexity and do not yield the correct solution. Therefore, Mark arrives at the correct answer.

Answer explanation

The correct formula for the distance between two points P1(x1,y1) and P2(x2,y2) is d=√((x2-x1)²+(y2-y1)²). This accounts for the differences in both x and y coordinates, making the first choice the right one.

Find the distance between the points (– 2, 0) and (4, 5).

• 61

• 62

Answer explanation

To find the distance between points (–2, 0) and (4, 5), use the distance formula: d = √[(x2 - x1)² + (y2 - y1)²]. Plugging in the values gives d = √[(4 - (-2))² + (5 - 0)²] = √[36 + 25] = √61.

Find the coordinates of the endpoints of the if the other endpoints is (5, -1) and the midpoints of segment is at (5, -5).

• (-9, 5)

• (-5, -9)

• (5, -9)

• (9, -5)

Answer explanation

To find the other endpoint, use the midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2). Given M(5, -5) and one endpoint (5, -1), we solve for the other endpoint (x2, y2). This gives (5, -9), which matches the correct answer.