Solution: Steps to construct: Step 1: Draw a regular hexagon of sides 4cm. Step 2: Draw the angle bisector of A and B. which intersects each other at point O. Step 3: Draw OL perpendicular to AB....
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.
Solution: Steps to construct: Step 1: Consider a point O on a line, with center O, and radius 3cm, draw a circle. Step 2: Extend its diameters on both sides and cut off OP = OQ = 7cm. Step 3: Mark...
Draw a line AB = 6 cm. Construct a circle with AB as diameter. Mark a point P at a distance of 5 cm from the mid-point of AB. Construct two tangents from P to the circle with AB as diameter. Measure the length of each tangent
Solution: Steps to construct: Step 1: Draw a line segment AB = 6cm. Step 2: Draw its perpendicular bisector bisecting it at point O. Step 3: With center O and radius OB, draw a circle. Step 4:...
Use a ruler and compass only in this question. (i) Draw a circle, centre O and radius 4 cm. (ii) Mark a point P such that OP = 7 cm. Construct the two tangents to the circle from P. Measure and record the length of one of the tangents.
Solution: Steps to construct: Step 1: Draw a circle with center O and radius 4cm and mark that point as A. Step 2: Take a point P such that OP = 7cm. Step 3: Bisect OB at M. Step 4: With center M...
(a) In the figure given below, AB is a diameter of the circle. If AE = BE and ∠ADC = 118°, find (i) ∠BDC (ii) ∠CAE
(B) inthe figure given below, AB is the diameter of the semi-circle ABCDE with centre O. If AE = ED and ∠BCD = 140°, find ∠AED and ∠EBD. Also Prove that OE is parallel to BD. Solution: (a) Join DB,...
(a) In figure (i) given below, triangle ABC is circumscribed, find x. (b) In figure (ii) given below, quadrilateral ABCD is circumscribed, find x.
(a) In figure (i) given below, triangle ABC is circumscribed, find x. (b) In figure (ii) given below, quadrilateral ABCD is circumscribed, find x. Solution: (a) From A, AP and AQ are the tangents...
Two concentric circles are of the radii 13 cm and 5 cm. Find the length of the chord of the outer circle which touches the inner circle.
Solution: Two concentric circles with center O OP and OB are the radii of the circles respectively, then OP = 5 cm, OB = 13 cm. Ab is the chord of outer circle which touches the inner circle at P....
The tangent to a circle of radius 6 cm from an external point P, is of length 8 cm. Calculate the distance of P from the nearest point of the circle.
Solution: Radius of the circle = 6 cm and length of tangent = 8 cm Let OP be the distance i.e. OA = 6 cm, AP = 8 cm . OA is the radius OA ⊥ AP Now In right ∆OAP, OP2 = OA2 + AP2 (By Pythagoras...
Find the length of the tangent drawn to a circle of radius 3cm, from a point distnt 5cm from the center.
Solution: In a circle with center O and radius 3cm and p is at a distance of 5cm. That is OT = 3 cm, OP = 5 cm OT is the radius of the circle OT ⊥ PT Now in right ∆ OTP, by Pythagoras axiom, OP2 =...
A and B are respectively the points on the sides PQ and PR of a triangle PQR such that PQ = 12.5 cm, PA = 5 cm, BR = 6 cm and PB = 4 cm. Is AB || QR? Give reasons for your answer.
Solution:- From the dimensions given in the question, Consider the ∆PQR So, PQ/PA = 12.5/5 = 2.5/1 PR/PB = (PB + BR)/PB = (4 + 6)/4 = 10/4 = 2.5 By comparing both the results, 2.5 = 2.5 Therefore,...
In the given figure, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. Prove that BM x NP = CN x MP.
Solution:- From the question it is given that, ABC is a triangle in which AB = AC. P is a point on the side BC such that PM ⊥ AB and PN ⊥ AC. We have to prove that, BM x NP = CN x MP Consider the...
Find the equation of a st. line perpendicular to the line 3x – 4y + 12 = 0 and having same y-intercept as 2x – y + 5 = 0.
Solution: Given line: 3x – 4y + 12 = 0 The slope of the line is given by 3x – 4y + 12 = 0 ⇒ 4y = 3x + 12 y = (3/4) x + 3 Thus, slope (m1) = ¾ Now, let the slope of the line perpendicular to the...