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The angle between tangent at a point P on circle and radius through the point is ___.
If PT is a tangent at T to a circle whose centre is O and OP = 17 cm, OT = 8 cm.
Find the length of the tangent segment PT.
If the quadrilateral sides touch the circle, prove that sum of pair of opposite sides is equal to the sum of other pair.
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle.
Prove that R bisects the arc PRQ.
Find the length of a tangent drawn to a circle with radius 5cm, from a point 13 cm from the center of the circle.
A point P is 26 cm away from O of circle and the length PT of the tangent drawn from P to the circle is 10 cm.
Find the radius of the circle.
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.
If from any point on the common chord of two intersecting circles, tangents be drawn to the circles, prove that they are equal.
Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at centre.
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.
Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.
In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the hypotenuse AC at P.
Prove that the tangent to the circle at P bisects BC.
From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of ∆PCD.
In the figure, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm.
Find the radius of its incircle.
Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc. u
From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that ∆APB is equilateral.
Two tangents segments PA and PB are drawn to a circle with centre O such that ∠APB = 120°.
Prove that OP = 2 AP.
If ∆ABC is isosceles with AB = AC and C (0, r) is the incircle of the ∆ABC touching BC at L.
Prove that L bisects BC.
In the figure, a circle touches all the four sides of a quadrilateral ABCD with AB = 6 cm, BC = 7 cm, and CD = 4 cm.
Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.
Two circles touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively.
Prove that TQ = TR.
A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ∆ABC.
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