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

Question

KnowledgeBoat · Accepted Answer

From figure, ∠ACB = ∠ADB (∵ angles in same segment are equal.) ....(i) ∠ACP = ∠ADP (∵ angles in same segment are equal.) ....(ii) We know, ∠ACP = ∠ACB (∵ CP bisects ∠ACB.) .....(iii) Using values from eq (i) and eq (ii) and putting in eq (iii) we get, ∠ADP = ∠ADB Hence, proved that DP bisects ∠ADB.

Mathematics

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

Circles

Related Questions

In figure (i) given below, P is the point of intersection of the chords BC and AQ such that AB = AP. Prove that CP = CQ.

In the figure (ii) given below, AB = AC = CD, ∠ADC = 38°. Calculate
(i) ∠ABC
(ii) ∠BEC.

In the figure (i) given below, chords AB and CD of a circle intersect at E.
(i) Prove that triangles ADE and CBE are similar.
(ii) Given DC = 12 cm, DE = 4 cm and AE = 16 cm, calculate the length of BE.

Mathematics

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

Circles

Related Questions

In figure (i) given below, P is the point of intersection of the chords BC and AQ such that AB = AP. Prove that CP = CQ.

In the figure (ii) given below, AB = AC = CD, ∠ADC = 38°. Calculate(i) ∠ABC(ii) ∠BEC.

In the figure (i) given below, chords AB and CD of a circle intersect at E.(i) Prove that triangles ADE and CBE are similar.(ii) Given DC = 12 cm, DE = 4 cm and AE = 16 cm, calculate the length of BE.

In the figure (ii) given below, AB = AC = CD, ∠ADC = 38°. Calculate
(i) ∠ABC
(ii) ∠BEC.

In the figure (i) given below, chords AB and CD of a circle intersect at E.
(i) Prove that triangles ADE and CBE are similar.
(ii) Given DC = 12 cm, DE = 4 cm and AE = 16 cm, calculate the length of BE.