Advertisements
Advertisements
Question
In the given figure, if ABC is an equilateral triangle. Find ∠BDC and ∠BEC.
Advertisements
Solution
It is given that, ABC is an equilateral triangle
We have to find `angleBDC` and `angleBEC`
Since ΔABC is an equilateral triangle
So, `angleA = angleB = angleC = 60°`
And ABEC is cyclic quadrilateral
So `angle A + angle E = 180°` (Sum of opposite pair of angles of a cyclic quadrilateral is 180°.)
Then,
`angle E = 180° - 60°`
= 120°
Similarly BECD is also cyclic quadrilateral
So,
`angle E + angle D = 180°`
`angleD = 180° - 120°`
= 60°
Hence, `angle BDC `= 60° and `angle BEC = 120°`.
APPEARS IN
RELATED QUESTIONS
Write True or False. Give reason for your answer.
A circle has only finite number of equal chords.
ture or false v
The degree measure of a semi-circle is 180°.
Prove that two different circles cannot intersect each other at more than two points.
In the given figure, O is the centre of a circle. PT and PQ are tangents to the circle from an external point P. If ∠TPQ = 70° , find the ∠TRQ.
In Fig. 1, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then the length of each tangent is:
Use the figure given below to fill in the blank:
If the length of RS is 5 cm, the length of PQ = _______
Construct a triangle PQR with QR = 5.5 cm, ∠Q = 60° and angle R = 45°. Construct the circumcircle cif the triangle PQR.
Construct a triangle ABC with AB = 5 cm, ∠B = 60° and BC = 6. 4 cm. Draw the incircle of the triangle ABC.
The ______________ is the longest chord of a circle
Which of the following describes the radius of a circle?
