[Hint: Draw a line through Q and perpendicular to QP.] As per the inquiry, Digressions PQ and PR are attracted to a circle to such an extent that ∠RPQ = 30°. A harmony RS is attracted corresponding...
In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Prove that the tangent to the circle at P bisects BC.
As per the inquiry, In a right point ΔABC is which ∠B = 90°, a circle is drawn with AB as distance across meeting the hypotenuse AC at P. Likewise PQ is a digression at P To Prove: PQ separates BC...
Two circles with centres O and O‘ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O‘P are tangents to the two circles. Find the length of the common chord PQ.
As per the inquiry, Two circles with focuses O and O' of radii 3 cm and 4 cm, individually meet at two focuses P and Q, to such an extent that OP and O'P are digressions to the two circles and PQ is...
If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in Fig. 9.17. Prove that ∠BAT = ∠ACB
As per the inquiry, A circle with focus O and AC as a measurement and AB and BC as two harmonies additionally AT is a digression at point A To Prove : ∠BAT = ∠ACB Verification : ∠ABC = 90° [Angle in...
From an external point P, two tangents, PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn which intersects PA and PB at C and D, respectively. If PA = 10 cm, find the perimeter of the triangle PCD.
As per the inquiry, From an outside point P, two digressions, PA and PB are attracted to a circle with focus O. At a point E on the circle digression is drawn which crosses PA and PB at C and D,...
Let s denote the semi-perimeter of a triangle ABC in which BC = a, CA = b, AB = c. If a circle touches the sides BC, CA, AB at D, E, F, respectively, prove that BD = s – b.
As indicated by the inquiry, A triangle ABC with BC = a , CA = b and AB = c . Likewise, a circle is engraved which contacts the sides BC, CA and AB at D, E and F individually and s is semi-border of...
If a hexagon ABCDEF circumscribe a circle, prove that AB + CD + EF = BC + DE + FA.
As per the inquiry, A Hexagon ABCDEF encompass a circle. To demonstrate: Stomach muscle + CD + EF = BC + DE + FA Verification: Digressions drawn from an outside highlight a circle are equivalent....
In Fig. 9.13, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.
As indicated by the inquiry, Abdominal muscle = CD Development: Produce AB and CD, to converge at P. Confirmation: Think about the circle with more noteworthy span. Digressions drawn from an outside...
Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.
Leave the lines alone l1 and l2. Expect that O contacts l₁ and l₂ at M and N, We get, OM = ON (Radius of the circle) In this way, From the middle "O" of the circle, it has equivalent separation from...
If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that angle DBC = 120°, prove that BC + BD = BO, i.e., BO = 2BC.
As per the inquiry, By RHS rule, ΔOBC and ΔOBD are harmonious By CPCT ∠OBC and ∠ OBD are equivalent In this way, \[\angle OBC\text{ }=\angle OBD\text{ }=60{}^\circ \] In triangle OBC, \[cos\text{...
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
We realize that, Sweep ⊥ Tangent = OR ⊥ PR i.e., ∠ORP = 90° Similarly, Sweep ⊥ Tangent = OQ ⊥PQ ∠OQP = 90° In quadrilateral ORPQ, Amount of every single inside point = 360º \[\angle ORP\text{...
Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle
From the figure, Harmony AB = 8 cm OC is opposite to the harmony AB AC = CB = 4 cm In right triangle OCA \[OC2\text{ }+\text{ }CA2\text{ }=\text{ }OA2\] \[OC2\text{ }=\text{ }52\text{ }\text{...
If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then OP = a√2.
True, Digression is consistently opposite to the span at the resource. Subsequently, ∠RPT = 90 Assuming 2 digressions are drawn from an outer point, they are similarly disposed to the line fragment...
The angle between two tangents to a circle may be 0°.
True, Defense: The point between two digressions to a circle might be 0°only when both digression lines concur or are corresponding to one another.
The length of tangent from an external point P on a circle with centre O is always less than OP.
True, Defense: Think about the figure of a circle with focus O. Leave PT alone a digression drawn from outer point P. Presently, Joint OT. OT ⏊ PT We realize that, Digression anytime on the circle...
The length of tangent from an external point on a circle is always greater than the radius of the circle.
False, Support: Length of digression from an outside point P on a circle might possibly be more prominent than the sweep of the circle.
If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.
False, Support: For instance, Think about the given figure. In which we have a circle with focus O and AB a harmony with ∠AOB = 60° Since, digression to any point on the circle is opposite to the...
At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is
(A) 4 cm (B) 5 cm (C) 6 cm (D) 8 cm As indicated by the inquiry, Span of circle, AO=OC = 5cm AM=8CM AM=OM+AO OM =AM-AO Subbing these qualities in the situation, OM= (8-5) =3CM OM is opposite to the...
From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
(A) 60 cm2 (B) 65 cm2 (C) 30 cm2 (D) 32.5 cm2 Development: Draw a circle of span 5 cm with focus O. Leave P alone a point a ways off of 13 cm from O. Draw a couple of digressions, PQ and PR. OQ...
In Fig. 9.4, AB is a chord of the circle and AOC is its diameter such that ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to
(A) 65° (B) 60° (C) 50° (D) 40° As per the inquiry, A circle with focus O, measurement AC and ∠ACB = 50° AT is a digression to the circle at point A Since, point in a half circle is a right point...
In Fig. 9.3, if AOB = 125°, then COD is equal to
(A) 62.5° (B) 45° (C) 35° (D) 55° ABCD is a quadrilateral delineating the circle We realize that, the contrary sides of a quadrilateral d elineating a circle subtend strengthening points at the...
If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is
(A) 3 cm (B) 6 cm (C) 9 cm (D) 1 cm As per the inquiry, OA = 4cm, OB = 5cm What's more, OA ⊥ BC Consequently, \[OB2\text{ }=\text{ }OA2\text{ }+\text{ }AB2\] \[\Rightarrow 52\text{ }=\text{...
If PA and PB are tangents from an outside point P. such that PA = 10 cm and ∠APB = 60°. Find the length of chord AB.
Given, $AP=10cm$ $\angle APB={{60}^{\circ }}$ According to the figure We know that, A line drawn from centre to point from where external tangents are drawn, bisects the angle made by tangents at...