Question

in the given adjoining figure ab is a diameter of a circle with centre o and cp is a tangent to a circle at point c. if ap=20cm, cp=10cm, find the radius of the circle

Answer 1

Answer: 7.5

Step-by-step explanation:

• Given,AP=20cm and CP=10cm.

• In the given figure, AP=AB+BP

                                      ⇒20=2r+BP

                                     ∴ BP=(20-2r)

• OP=BP+OB

     ⇒OP=20-2r+r

     ⇒OP=(20-r)

• In right ΔOCP

       $OP^{2}=OC^{2}+CP^{2}$

    ⇒$(20-r)^{2}=r^{2}+10^{2}$

    ⇒$400+r^{2}-40r=r^{2}+100$

    ⇒400-100=40r

    ⇒300=40r

    ⇒r=$\frac{300}{40}$

    ∴ r =7.5cm

• Hence,radius of the circle is 7.5cm.

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