(d) POR is an isosceles triangle with PQ = PR, and angle QPR **”. Angle POR = (2x +30)” OR – (p+3)cm PO = (2+3) cm Find

Question

(d) POR is an isosceles triangle with PQ = PR, and angle QPR **”.
Angle POR = (2x +30)”
OR – (p+3)cm
PO = (2+3) cm
Find an expression for the perimeter of the triangle in terms of p,
giving your answer in its simplest form.

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Natalia 3 months 2021-11-10T19:28:26+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-10T19:29:43+00:00

    Answer:

    1) It is given that line AB is tangent to the circle at A.

    ∴ ∠CAB = 90º (Tangent at any point of a circle is perpendicular to the radius throught the point of contact)

    Thus, the measure of ∠CAB is 90º.

    (2) Distance of point C from AB = 6 cm (Radius of the circle)

    (3) ∆ABC is a right triangle.

    CA = 6 cm and AB = 6 cm

    Using Pythagoras theorem, we have

    BC2=AB2+CA2⇒BC=62+62−−−−−−√ ⇒BC=62–√ cm

    Thus, d(B, C) = 62–√ cm

    (4) In right ∆ABC, AB = CA = 6 cm

    ∴ ∠ACB = ∠ABC (Equal sides have equal angles opposite to them)

    Also, ∠ACB + ∠ABC = 90º (Using angle sum property of triangle)

    ∴ 2∠ABC = 90º

    ⇒ ∠ABC = 90°2 = 45º

    Thus, the measure of ∠ABC is 45º.

    Step-by-step explanation:

    i hope this answer is useful

    and this question is too good

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