Geometry Module 9 Test - Form A

The sides of ΔFHG are tangent to circle P at points M, N, and O as shown in the diagram. Which statement is true?

• The altitudes of the triangle are concurrent at point P.

• The angle bisectors of the triangle are concurrent at point P.

• The medians of the triangle are concurrent at point P.

• The perpendicular bisectors of the triangle are concurrent at point P.

Answer explanation

In a triangle, an altitude is a line segment drawn from a vertex perpendicular to the opposite side (or its extension), forming a right angle, and is also known as the height of the triangle. 

In a triangle, a median is a line segment joining a vertex to the midpoint of the opposite side, and every triangle has exactly three medians, which intersect at the centroid

A circle with center P is circumscribed about ΔHJK. Point A is the midpoint of HJ. If AP = 4.5 in. and HJ = 45 in., what is the approximate radius of the circle?

• 22.5 in.

• 23.0 in.

• 45.0 in.

• 49.5 in.

Answer explanation

The radius of the circle circumscribed about

△HJK triangle cap H cap J cap K

△𝐻𝐽𝐾. 

What's given in the problem 

• AP=4.5cap A cap P equals 4.5

  𝐴𝑃=4.5 in.

• HJ=45cap H cap J equals 45

  𝐻𝐽=45in.

  𝐴 is the midpoint of

  HJ.

• Helpful information 

  The radius of a circle circumscribed about a triangle is the distance from the center of the circle to any vertex of the triangle.

  • A line segment from the center of a circle to the midpoint of a chord is perpendicular to the chord.

  • Pythagorean theorem:

    a2+b2=c2. a squared plus b squared equals c squared

    𝑎2+𝑏2=𝑐2, where

    𝑎 and 𝑏 are the legs of a right triangle and𝑐 is the hypotenuse.

  • How to solve

    Use the Pythagorean theorem to find the radius of the circle.

  • Step 1.Find the length of AH.

The circumcenter of ΔRST is at a point outside of the triangle. What type of triangle is ΔRST?

• acute

• obtuse

• right

• equiangular

The centroid of ΔABC is point P. Point M is the midpoint of BC, and MP = 252 cm. What is the length of AP?

• 126 cm

• 168 cm

• 504 cm

• 756 cm

In ΔEFG, m∠E = (8x + 5)°, m∠F = (x − 11)°, and m∠G = (2x − 1)°. What is m∠E to the nearest degree?

• m∠E = 141°

• m∠E = 90°

• m∠E = 88°

• m∠E = 87°

The vertices of ΔWXY are located at W(−14, 20), X(10, 4), and Y(−2, −4). What is the approximate length of the midsegment parallel to XY?

• 4.8 units

• 7.2 units

• 9.3 units

• 14.4 units

In ΔABC, m∠A = 92°, m∠B = 55°. What is m∠C to the nearest degree?

• m∠C = 33°

• m∠C = 35°

• m∠C = 30°

• m∠C = 28°

The perpendicular bisectors of the sides of ΔJKL intersect at point P. If JP = 2x + 5 meters and KP = 4x − 13 meters, what is the length of LP to the nearest meter?

• LP = 23 meters

• LP = 10 meters

• LP = 11 meters

• LP = 12 meters

In the figure, D, C, and B are collinear. What is the measure of ∠A to the nearest degree?

• ∠A = 41°

• ∠A = 30°

• ∠A = 57°

• ∠A = 60°

In the figure, ED = 3x + 5 cm and DF = 2(x + 8) cm. For what value of x does BD bisect ∠ABC?

• x = 11

• x = 10

• x = 12

• x = 9