We read your photo as:

A circle has a radius of 3 cm. Draw a diameter AB. Construct AC = 4.5 cm such that C is on the circle. Connect BC and measure its length.

Mathematics

ScanSolve AI Answer

Answers

2 parts
d

3.97 cm3.97 \text{ cm}

e

90∘90^\circ

Step-by-step solution

8 steps

It looks like part a) of the question, which likely involved drawing the initial circle, is missing. I will assume you have drawn a circle with a radius of 3 cm3 \text{ cm} (so the diameter is 6 cm6 \text{ cm}) to proceed with the following steps.

Part b· 2 steps

Draw a diameter AB

  1. Locate the center of your circle.

  2. Draw a straight line segment passing through the center of the circle and touching the circle at two points.

    Label these points A and B. This line segment AB is the diameter.

Part c· 4 steps

Construct AC = 4.5 cm such that C is on the circle

  1. Place the compass point at A.

  2. Open the compass to a radius of 4.5 cm4.5 \text{ cm}.

  3. Draw an arc that intersects the circle.

    Label one of the intersection points as C.

  4. Draw a straight line segment from A to C.

    This segment AC will be 4.5 cm4.5 \text{ cm} long.

Part d

3.97 cm3.97 \text{ cm}

Connect BC and measure its length

  1. Draw a straight line segment connecting point B to point C.

  2. Measure the length of the segment BC using a ruler.

    Calculation based on assumed diameter:
    If the diameter AB=6 cmAB = 6 \text{ cm} and AC=4.5 cmAC = 4.5 \text{ cm}, then △ABC\triangle ABC is a right-angled triangle with the right angle at C (angle in a semicircle).
    Using the Pythagorean theorem (AB2=AC2+BC2AB^2 = AC^2 + BC^2):

    (6 cm)2=(4.5 cm)2+BC2(6 \text{ cm})^2 = (4.5 \text{ cm})^2 + BC^2 36 cm2=20.25 cm2+BC236 \text{ cm}^2 = 20.25 \text{ cm}^2 + BC^2 BC2=36 cm2−20.25 cm2BC^2 = 36 \text{ cm}^2 - 20.25 \text{ cm}^2 BC2=15.75 cm2BC^2 = 15.75 \text{ cm}^2 BC=15.75 cmBC = \sqrt{15.75} \text{ cm} BC≈3.97 cmBC \approx 3.97 \text{ cm}

    You should measure approximately 3.97 cm\boxed{3.97 \text{ cm}}.

Part e

90∘90^\circ

State the value of angle ACB

The angle subtended by a diameter at any point on the circumference of a circle is always a right angle. Since AB is the diameter and C is a point on the circumference, ∠ACB\angle ACB is the angle subtended by the diameter.
The value of angle ACB is 90∘\boxed{90^\circ}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QBased on the measurements provided in the figure: AB = 2.7 cm, BC = 1.5 cm, and the total length AD…QGiven AB = 3 cm and BC = 4 cm, and ABC = 90^.QConstruct a circle with radius 4 cm. Draw a diameter PT. Construct a tangent at T. Mark a point R on…QA chord AB of length 300 mm is at a distance of 100 mm from the center of a circle. Find the radius…QConstruct a circle that touches points ABC. What is the radius of the circle? (3mks)
Browse by topic:Geometry
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp