Mathematics
Use ruler and compass for the following construction:
(a) construct an equilateral triangle ABC of side 5 cm.
(b) construct the circumcircle of ΔABC.
(c) construct the locus of points which are equidistant from AB and BC. Mark the point where the circumcircle and locus meet, as D.
(d) give the geometrical name of quadrilateral ABCD.
Answer
Steps of construction :
Draw a line segment AB = 5 cm.
At point A with radius = 5 cm draw an arc.
At point B with radius = 5 cm draw another arc, cutting previous arc at point C.
Join AC and BC.
Construct perpendicular bisectors of AB and BC, let the bisectors meet at point O.
With O as centre and OA as radius draw a circumcircle.
Construct angle bisector of ∠ABC, mark the point as D where angle bisector intersects circumcircle.
Join AD and CD.
Since, points A, B, C and D lie on the circumcircle, thus ABCD is a cyclic quadrilateral.
Hence, ABCD is a cyclic quadrilateral.
Related Questions
The polynomial kx3 + 3x2 − 11x − 6 when divided by (x + 1), leaves a remainder of 6.
(a) Find the value of k.
(b) Using the value of k factorise completely the polynomial kx3 + 3x2 − 11x − 6.
Prove that :
(sec θ − cos θ)(cosec θ − sin θ) = sin θ cos θ
The cost price of a TV set is ₹ 20,000. The shopkeeper marked it for ₹ 24,000. He sells it to a customer at a discount of 10% on the marked price. If the sale is intra-state and the rate of GST is 12%, find the:
(a) discounted price of the TV set.
(b) amount paid by the customer to clear the bill.