In figure, the sides AB, BC and CA of triangle ABC touch a circle with centre O and radius r at P, Q and R respectively.Prove that
(i) AB + CQ = AC + BQ
(ii)area (\(\Delta\)ABC) = \(1\over2\) (perimeter of \(\Delta\)ABC) x r

4

(a)

Two circles touch each other externally at C.AB and CD are two common tangents.If D lies on AB such that CD=6cm, then find AB.

4

(a)

QR is a tangent Q.PR||AQ, where AQ is a chord through A and P is a centre, the end point of the diameter AB.Prove that BR is tangent at B.

4

(a)

In the given figure, the diameters, of two wheels have measures 4cm and 2cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angles.

4

(a)

With the vertices of a triangle ABC as centres, three circles are described each touching the other two externally. If the sides of the triangle are 4 cm, 6 cm, and 8 cm, find the radii of the circles.

4

(a)

PA and PB are two tangents from an exterior point P to a circle of radius 5 cm. If length of the chord AB is 8 cm, then find the length of the tangent.

4

(a)

If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that \(\angle DBC={ 120 }^{ \circ }\), prove that BC + CD = BO i.e., BO = 2BC.

4

(a)

Choose the correct option and given justification:
In the given figure, if TP and TO are the two tangents to a circle with centre O, so that  \(\angle\)POQ = 110°, then  \(\angle\)PTO is equal to

(a) \(60^{ \circ }\)
(b) \(70^{ \circ }\)
(c)  \(80^{ \circ }\)
(d) \(90^{ \circ }\)​​​​​​​

4

(a)