The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC. Write ‘True’ or ‘False’ and justify your answer
Solution:
Consider a circle in which EF is a tangent passing through point A on the circle and ABC is an isosceles triangle in the circle, in which AB = AC
To Prove: EF || BC
Construction: Join OA , OB and OC
Proof:
AB = AC [Given]
Angles opposite to equal sides are equal
∠ACB = ∠ABC --- [1]
Since we know that the angle between the chord and the tangent is equal to the angle made by the chord in the alternate segment
Therefore,
∠EAB = ∠ACB --- [2]
From [1] and [2]
∠EAB = ∠ACB
Two lines are parallel if their alternate interior angles are equal
EF || BC
Therefore, the statement is true.
✦ Try This: If D, E and F are respectively, the mid-points of AB, AC and BC in ΔABC, then BE + AF is equal to
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.2 Problem 7
The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC. Write ‘True’ or ‘False’ and justify your answer
Summary:
The statement “The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to BC” is true
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