Question

A triangle ABC has been inscribed in a circle. The bisectors of <A, <B and <C meet the circle at P, Q and R respectively. If <BAC = 50°, find <QPR.​

Answer 1

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A triangle ABC has been inscribed in a circle. The bisectors of <A, <B and <C meet the circle at P, Q and R respectively. If <BAC = 50°, find <QPR.

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<BAP = <PAC = 25°

<OBC 1/2< ABC

RCB=<ACB(as AP, BO and CR bisect <BAC,< ABC and <ACB respectively).

<BOP = <BAP -25°,

ZPRC = 2PAC = 25 ORC - OBC ABC,

<RQB=<RCB=1/2<ACB

(as the angles in the same segment of a circle are equal).

<BQP = <RQB + <BOP 1/2<ACB + 25°

<QRP = <QRC + PRC = 1/2<ABC + 25°

<QPR=180°-(<RQP+<QRP)

<QPR=180°-(1/2<ACB+25°+ 1/2<ABC+25°)

<QPR=180°-1/2(<ACB+<ABC) -50°

<QPR=130°-1/2(180°-<BAC)

<QPR=130°-1/2(180°-50°)

<QPR=130°-1/2×130

<QPR =130°-65°

<QPR=65°.

Answer 2

Answer:

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