Equilateral Triangle Inscribed

We will prove that, PQR is an equilateral triangle inscribed in a circle. The tangents at P, Q and R form the triangle P’Q’R’. Prove that P’Q’R’ is also an equilateral triangle.

Equilateral Triangle Inscribed



PQR is an equilateral triangle inscribed in a circle whose centre is O. Three tangents are drawn to the circle at the points P, Q and R. They intersect pair wise at P’, Q’ and R’.

To prove: P’Q’R’ is an equilateral triangle.




1. ∠Q’PR = ∠PQR.

∠Q’RP = ∠PQR.

1. Angle between tangent and chord is equal to the angle in the alternate segment.

2. ∠PQR = 60°

2. Each angle of the equilateral triangle PQR has the measure 60°.

3. ∠Q’PR = ∠Q’RP = 60°.

3. By statements 1 and 2.

4. ∠PQ’R = 180° – (∠Q’PR + Q’RP)

             = 180° – (60° + 60°) = 60°.

4. Sum of three angles of a triangle is 180.

5. Similarly, ∠PR’Q = 60°

                and ∠QP’R = 60°.

5. Similar reason.

6. ∆P’Q’R’ is equilateral.

6. By statements 4 and 5.

10th Grade Math

From Equilateral Triangle Inscribed to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Types of Fractions |Proper Fraction |Improper Fraction |Mixed Fraction

    Mar 02, 24 05:31 PM

    The three types of fractions are : Proper fraction, Improper fraction, Mixed fraction, Proper fraction: Fractions whose numerators are less than the denominators are called proper fractions. (Numerato…

    Read More

  2. Subtraction of Fractions having the Same Denominator | Like Fractions

    Mar 02, 24 04:36 PM

    Subtraction of Fractions having the Same Denominator
    To find the difference between like fractions we subtract the smaller numerator from the greater numerator. In subtraction of fractions having the same denominator, we just need to subtract the numera…

    Read More

  3. Addition of Like Fractions | Examples | Worksheet | Answer | Fractions

    Mar 02, 24 03:32 PM

    Adding Like Fractions
    To add two or more like fractions we simplify add their numerators. The denominator remains same. Thus, to add the fractions with the same denominator, we simply add their numerators and write the com…

    Read More

  4. Comparison of Unlike Fractions | Compare Unlike Fractions | Examples

    Mar 01, 24 01:42 PM

    Comparison of Unlike Fractions
    In comparison of unlike fractions, we change the unlike fractions to like fractions and then compare. To compare two fractions with different numerators and different denominators, we multiply by a nu…

    Read More

  5. Equivalent Fractions | Fractions |Reduced to the Lowest Term |Examples

    Feb 29, 24 05:12 PM

    Equivalent Fractions
    The fractions having the same value are called equivalent fractions. Their numerator and denominator can be different but, they represent the same part of a whole. We can see the shade portion with re…

    Read More