Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

3

(a)

In the given figure, ABC is a right-angled triangle, right angled at A, with AB =6cm and AC=8cm.A circle with centre O has been inscribed inside the triangle Calculate the value of r, the radius of the inscribed circle.

3

(a)

ABC is a right-angled triangle, right angled at A.A circle is inscribed in it.The lengths of two sides containing the angle are 24cm and 10cm.Find the radius of the incircle.

3

(a)

In two concentric circles, a chord of length 24 cm of larger circle becomes a tangent to the smaller circle whose radius is 5 cm. Find the radius of the larger circle.

3

(a)

AB is a diameter of a circle. AH and BK are perpendicular from A and B respectively to the tangent at P.Prove that AH + BK = AB.

3

(a)

In fig., if \(\angle ATO={ 40 }^{ \circ }\), find\(\angle AOB\). 

3

(a)

Two tangents are drawn to a circle from an external point A, touching the circle at B and C. From another point L, a third tangent is drawn to the circle intersecting AB in P and AC in R and touching the circle at Q. If AB = 32 cm, find the perimeter of \(\triangle APR\).

3

(a)

The lengths of tangents drawn from an external point to a circle are equal.

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(a)

If PA and PB are two tangents drawn from a point P to a circle with centre O touching it at A and B, prove that OP is perpendicular bisector of AB.

3

(a)

What will you call a line, if it intersect a circle at two distinct points?

3

(a)

Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle, is bisected at the point of contact.

3

(a)

ABCD is a quadrilateral such that \(\angle D=90^{ \circ }\). A circle C (O, r) touches the sides AB, BC, CD and DA at P, Q, R and S, respectively. If BC = 38 cm, CD = 25 cm and BP = 27 cm, then find the value of r.

3

(a)

In the given figure, PA and PB are tangents to the given circle such that PA = 5 cm and \(\angle APB={ 60 }^{ \circ }\). Find the length of chord AB.

3

(a)

A circle is inscribed in a ΔBC having sides AB=8 cm, BC = 10 cm and CA  = 12 cm as shown in figure. Find AD, BE and CF

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(a)