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In the figure (i) given below, CP bisects ∠ACB. Prove that DP bisects ∠ADB.

In the figure (i) given below, CP bisects ∠ACB. Prove that DP bisects ∠ADB. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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Answer

From figure,

∠ACB = ∠ADB (∵ angles in same segment are equal.) ….(i)

∠ACP = ∠ADP (∵ angles in same segment are equal.) ….(ii)

We know,

∠ACP = 12\dfrac{1}{2}∠ACB (∵ CP bisects ∠ACB.) …..(iii)

Using values from eq (i) and eq (ii) and putting in eq (iii) we get,

∠ADP = 12\dfrac{1}{2}∠ADB

Hence, proved that DP bisects ∠ADB.

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