In Fig 10.57, a circle is inscribed in a quadrilateral ABCD in which . If AD = 23 cm, AB = 29 cm and DS = 5 cm, find the radius r of the circle.
AD = DS = 5cm (tangent from an external point)
Since AD=23 cm
AR + RD + AD
AR + 5 = 23 cm
AR = 18 cm ------(i)
and AQ = AR
since AR = 18 cm
So, AQ + QB = AB
Now OP and OQ are radius of the circle. So from tangent P and Q
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PREVIOUSTwo 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 NEXTIn Fig. 10.58, there are two concentric circles with centre O of radii 5 cm and 3 cm. from an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP.
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